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1. JSTOR Representation Theory For Polyadic Algebras.
This is a direct generalization of the corresponding result of Halmos for locally finite Polyadic algebras of infinite degree.
http://links.jstor.org/sici?sici=0022-4812(196409)29:3<148:RTFPA>2.0.CO;2-U

2. IngentaConnect On Amalgamation Of Reducts Of Polyadic Algebras
G Polyadic algebras are obtained by restricting the (similarity type and) axiomatization of dimensional Polyadic algebras to finite quantifiers and
http://www.ingentaconnect.com/content/klu/12/2004/00000051/00000004/art00001
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3. Note On Cylindric Algebras And Polyadic Algebras.
Note on cylindric algebras and Polyadic algebras. A. H. Copeland. Source Michigan Math. J. Volume 3, Issue 2 (1955), 155157. Primary Subjects 02.0X
http://projecteuclid.org/handle/euclid.mmj/1028990028
Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options

4. Information Algebra - Wikipedia, The Free Encyclopedia
Reducts of cylindrical algebras (Henkin, Monk Tarski 1971) or Polyadic algebras are information algebras related to predicate logic (Halmos 2000) .
http://en.wikipedia.org/wiki/Information_Algebra
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
Information algebra
From Wikipedia, the free encyclopedia
(Redirected from Information Algebra Jump to: navigation search Classical information theory goes back to Claude Shannon . It is a theory of information transmission, looking at communication and storage. However, it has not been considered so far that information comes from different sources and that it is therefore usually combined. It has furthermore been neglected in classical information theory that one wants to extract those parts out of a piece of information that are relevant to specific questions. A mathematical phrasing of these operations leads to an algebra of information , describing basic modes of information processing. Such an algebra grasps a lot of formalisms of computer science , which seem to be different on the surface: relational databases, multiple systems of formal logic or numerical problems of linear algebra. It allows the development of generic procedures of information processing and thus a unification of basic methods of computer science, in particular of distributed information processing.
Contents
edit Information algebra
Information relates to precise questions, comes from different sources, must be aggregated and can be focused on questions of interest. Starting from these considerations

5. Preprints Of The Algebraic Logic Dept.
Gábor Sági Noncomputability of the consequences of the axioms of the omega-dimensional Polyadic algebras. Abstract dvi version PostScript version
http://www.math-inst.hu/pub/algebraic-logic/Contents.html
Preprints of the Algebraic Logic Department
Please note that this page (and the ftp site of the AL dept.) contains only a subset of the papers that are available electronically. If you know of a paper by a member of the dept., and would like to see it here, contact him/her. If you have problems retrieving a paper listed here, please let me know.

6. Algebraic Logic - Elsevier
Halmos (Polyadic) algebras in Database Theory. Characterizing Relativized Cylindric algebras. Strictly Finite Schema Axiomatization of QuasiPolyadic
http://www.elsevier.com/wps/product/librarians/523236
Home Site map Elsevier websites Alerts ... Algebraic Logic Book information Product description Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view ALGEBRAIC LOGIC
Edited by
J.D. Monk
Included in series
Colloquia Mathematica Societatis Janos Bolyai, 54
Description
Contents
Hardbound, ISBN: 0-444-88543-9, vi + 746 pages, publication date: 1991
Imprint: NORTH-HOLLAND
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
See also information about , and links to our regional sales offices Last update: 11 Dec 2007 Scroll(200, 120, 120,'Out of print'); Book contents Table of contents Reviews Submit your review Bookmark this page Recommend this publication Overview of all books ... Feedback A Reed Elsevier company Elsevier B.V.

7. Relation Algebras From Cylindric And Polyadic Algebras
Relation algebras from Cylindric and Polyadic algebras. István Németi, András Simon. Journal Title Logic Journal of the IGPL. Date 1997. Volume 5
http://wotan.liu.edu/docis/show?doc=dbl/ljigpl/1997_5_4__RAFCAP.htm&query=algebr

8. CiteULike: On Amalgamation Of Reducts Of Polyadic Algebras
On amalgamation of reducts of Polyadic algebras algebra universalis, Vol. 51, No. 4. (August 2004), pp. 301359. Citation format
http://www.citeulike.org/article/641133
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algebra universalis , Vol. 51, No. 4. (August 2004), pp. 301-359. Citation format: Plain APA Chicago Elsevier Harvard MLA Nature Oxford Science Turabian Vancouver
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9. Baztech Informacja O Publikacji
Streszczenie angielskie Lambda abstraction algebras are designed to algebraize the untyped lambda calculus in the same way cylindric and Polyadic algebras
http://baztech.icm.edu.pl/baztech/cgi-bin/btgetdoc.cgi?BUS1-0003-0024

10. EMail Msg <9407221103.AA03846@rodin.wustl.edu>
Yes Polyadic algebras are due to Halmos. If there is an _intensional_ theory of subsumption of composite relational structures, I don t know of it.
http://www-ksl.stanford.edu/email-archives/srkb.messages/274.html
Re: The "Minsky bottleneck" ...and a solution?
fritz@rodin.wustl.edu (Fritz Lehmann) Date: Fri, 22 Jul 94 06:03:05 CDT From: fritz@rodin.wustl.edu (Fritz Lehmann) Message-id: Newsgroups: comp.ai,sci.logic,alt.sci.physics.new-theories Subject: Re: The "Minsky bottleneck" ...and a solution? References: <30g0h5$g18@bigfoot.wustl.edu> <30hira$nid@mercury.mcs.com> <30i4ho$ Apparently-To: s@wugate.wustl.edu Apparently-To: cbrink@ucthpx.uct.ac.za Apparently-To: srkb@cs.umbc.edu Apparently-To: interlingua@isi.edu Apparently-To: cg@cs.umn.edu Sender: owner-srkb@cs.umbc.edu Precedence: bulk

11. Relation Algebras From Cylindric And Polyadic Algebras
This paper is a survey of recent results concerning connections between relation algebras (RA), cylindric algebras (CA) and Polyadic equality algebras (PEA)
http://nsdl.org/resource/2200/20061012021614925T
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12. Abstracts Of Fundamenta Informaticae Volume 32. Number 1
Lambda abstraction algebras are designed to algebraize the untyped lambda calculus in the same way cylindric and Polyadic algebras algebraize the
http://fi.mimuw.edu.pl/abs32.html
Abstracts of Fundamenta Informaticae Volume 32.
Number 1
M. F. FRIAS , G. A. BAUM and A. M.HAEBERER
Fork Algebras in Algebra, Logic and Computer Science pages 125

Since the main themes at the Helena Rasiowa memorial were algebra, logic and computer science, we will present a survey of results on fork algebras from
these points of view. IIn this paper we study fork algebras from the points ofview of their algebraic and logical properties and applications. These results
will prove to be essential, in a future work, for the definition of a wide-spectrum calculus for program construction.
S. KASANGIAN and S. VIGNA
The Topos of Labelled Trees: A Categorical Semantics for SCCS pages 27-45

In this paper a we give a semantics for SCCS using the constructions of the topos of labelled trees. The semantics accounts for all aspects of the original
formulation of SCCS including unbounded non-determinism. Then, a partial solution to the problem of characterizing bisimulation in terms of a class of morphisms is proposed. We define a class of morphisms of the topos of trees, called conflict preserving , such that two trees T and U are bisimilar iff there is a pair of conflict preserving morphisms f from T to U and g from U to T such that fgf=f and gfg=g . It is the first characterization which does not require the existence of a third quotient object. The results can be easily extended to more general transition systems. D. PIGOZZI and A. SALIBRA

13. Berti, Massimiliano
Distinguished algebras of logic 10.1 Cylindric algebras. 10.2 Relation algebras, substitution cylindric algebras, Polyadic algebras.- 10.3 Relativization.
http://www.yurinsha.com/410/p6.htm

14. From MAILER-DAEMON Fri May 18 091452 2007 Date 18 May 2007 09
Another version of equivalence results can be obtained if we replace CAs by Polyadic algebras introduced by Halmos. One more delicate point is that CAs are
http://www.mta.ca/~cat-dist/archive/2007/07-5
From MAILER-DAEMON Fri May 18 09:14:52 2007 Date: 18 May 2007 09:14:52 -0300 From: Mail System Internal Data Subject: DON'T DELETE THIS MESSAGE FOLDER INTERNAL DATA Message-ID: X-IMAP: 1178037477 0000000026 Status: RO This text is part of the internal format of your mail folder, and is not a real message. It is created automatically by the mail system software. If deleted, important folder data will be lost, and it will be re-created with the data reset to initial values. From rrosebru@mta.ca Tue May 1 12:12:36 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 01 May 2007 12:12:36 -0300 Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HityA-0003Au-KA for categories-list@mta.ca; Tue, 01 May 2007 12:08:46 -0300 Date: Tue, 1 May 2007 08:53:18 -0400 (EDT) From: Michael Barr To: Categories list Subject: categories: Tensor products (and C*-algebras) MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Sender: cat-dist@mta.ca Precedence: bulk Message-Id: Status: O X-Status: X-Keywords: X-UID: 1 I think it important to note that tensor products have no universal mapping property and no categorical definition. Given an internal hom, there might or might not be a tensor product that provides a left adjoint for it. Given a bifunctor, there might or might not be an internal hom (or two if the bifunctor is not symmetric) right adjoint to it. Another point is that the tensor product on abelian groups (or modules over any commutative right) has two universal mapping properties: It provides left adjoints for the quite obvious (but still not categorically defined) internal hom and also represents the functor that takes A to the functor of bilinear maps out of A x B. In any case, it makes no sense to ask what is the "right" tensor product. The right tensor product will be the one that is appropriate to the job you want to do with it. Michael From rrosebru@mta.ca Tue May 1 13:44:02 2007 -0300 Return-path:

15. OUP: UK General Catalogue
Predicates, terms, and operations in Polyadic algebras Terms and Equality Predicates, terms, operations, and equality in Polyadic Boolean algebras
http://www.oup.com/uk/catalogue/?ci=9780821841389

16. [Geo80] Generalized Quantifiers On Polyadic Algebras
volume = {25}, title = {Generalized quantifiers on Polyadic algebras}, year = {1980}, fjournal = {Acad\ emie de la R\ epublique Populaire Roumaine.
http://www.mathematik.tu-darmstadt.de/~leustean/GLAU/bib2html/output/entry-Geo-8
Overview Tree Index Bibliography PREV NEXT FRAMES NO FRAME
[Geo80] Generalized quantifiers on polyadic algebras
Geo:80b (Article) Author(s) Georgescu, George Title Journal Rev. Roumaine Math. Pures Appl. Volume Number Page(s) Year BibTeX code Overview Tree Index Bibliography PREV NEXT FRAMES NO FRAME Submit a bug This document was generated by
Stephane GALLAND (under the GNU General Public License

17. JSTOR Nonhomogeneous Polyadic Algebras
NONHOMOGENEOUS Polyadic algebras LEON LEBLANC Introduction. In a series of papers 14 Halmos introduced the theory of homogeneous Polyadic algebras.
http://spider.jstor.org:9080/spidergate/article?sici=0002-9939(196202)13:1<59:NP

18. Scientific Commons An Autobiography Of Polyadic Algebras (2000
An Autobiography of Polyadic algebras (2000). Paul R. Halmos. Abstract. rence.) I liked symbolic logic the same way as I liked algebra simplifying an
http://de.scientificcommons.org/507145

19. PDF: A Categorical Approach To Polyadic Algebras - AcrobatFiles.com
Download A categorical approach to Polyadic algebras at AcrobatFiles.com.
http://www.acrobatfiles.com/mathematics/238-11827-pdf.html
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20. Read This: Logic As Algebra
It certainly leads naturally into Halmos s Algebraic Logic, which develops the theory of multiple quantifiers via Polyadic algebras.
http://maa.org/reviews/logalg.html
Read This!
The MAA Online book review column
Logic as Algebra
by Paul Halmos and Steven Givant
Reviewed by Mark Johnson
The intent of Logic as Algebra is expressed clearly in its preface: ...to show that logic can (and perhaps should) be viewed from an algebraic perspective. When so viewed, many of its principal notions are seen to be old friends, familiar algebraic notions that were "disguised" in logical clothing. Moreover, the connection between the principal theorems of the subject and well-known theorems in algebra becomes clearer. Even the proofs often gain in simplicity. To this end, authors Paul Halmos and Steven Givant have written a brief, engaging text aimed at both amateurs and professionals, which requires only a course in modern algebra as background. Since one of this book's potential uses is as a course text, an outline of its contents may be helpful:
  • What is Logic?
    An introductory parable and mini-logic prepare the reader to meet propositional logic.
  • Propositional Calculus
    A fairly traditional development of propositional logic.

21. DBLP: István Németi
44, István Németi, Gábor Sági On The Equational Theory of Representable Polyadic Equality algebras. J. Symb. Log. 65(3) 11431167 (2000)
http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/n/N=eacute=meti:Istv=a
List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... EE : Can General Relativistic Computers Break the Turing Barrier?. CiE 2006 EE : New Physics and Hypercomputation. SOFSEM 2006 EE : Relativistic computers and the Turing barrier. Applied Mathematics and Computation 178 EE Math. Log. Q. 51 Tarek Sayed Ahmed ... Fundam. Inform. 44 : On The Equational Theory of Representable Polyadic Equality Algebras. J. Symb. Log. 65 Ian M. Hodkinson J. Symb. Log. 64 Steven Givant : Notions of Density That Imply Representability in Algebraic Logic. Ann. Pure Appl. Logic 91 Robert Goldblatt J. Symb. Log. 63 EE : On the Equational Theory of Representable Polyadic Equality Algebras. Logic Journal of the IGPL 6 Ian M. Hodkinson RelMiCS 1997 EE ... EE : Relation Algebras from Cylindric and Polyadic Algebras. Logic Journal of the IGPL 5 Steven Givant J. Symb. Log. 60 J. Symb. Log. 60 : Decidable and Undecidable Logics with a Binary Modality. Journal of Logic, Language and Information 4 Maarten Marx Journal of Logic, Language and Information 4 Math. Log. Q. 41 ... J. Symb. Log. 59 : Applying Algebraic Logic to Logic. AMAST 1993 : On the Strength of Temporal Proofs.

22. [Abstract] Software Verification In An Algebraic Setting
19 L. Leblanc, Nonhomogeniuos Polyadic algebras, Proc. American Mathematical Society, 13(1), 1962, 59 65. 20 E.M. Beniaminov, An algebraic approach to
http://actapress.com/PDFViewer.aspx?paperId=14578

23. Intute Harvester - Search Results
ON THE EQUATIONAL THEORY OF REPRESENTABLE Polyadic EQUALITY algebras. I. Németi, G. Relation algebras from cylindric and Polyadic algebras
http://www.intute.ac.uk/cgi-bin/search_harvester.pl?term1=polyadic&subject=scien

24. Atlas: On Representation Of Cylindric Algebras By Miklos Ferenczi
The natural algebraizations of first order logic e.g. locally finite cylindric (or locally finite quasi Polyadic) algebras do not form a variety.
http://atlas-conferences.com/c/a/o/c/17.htm
Atlas home Conferences Abstracts about Atlas Algebras, Lattices, Varieties - A Conference in Honor of Walter Taylor
August 15-18, 2004
University of Colorado
Boulder, Colorado, USA Organizers
Jennifer Hyndman, Keith Kearnes, Ralph McKenzie, George McNulty, Ágnes Szendrei, Ross Willard View Abstracts
Conference Homepage On representation of cylindric algebras
by
Miklos Ferenczi
Budapest University of Technology, Department of Algebra The natural algebraizations of first order logic e.g. locally finite cylindric (or locally finite quasi polyadic) algebras do not form a variety. Omitting the locally finiteness we get a variety but representability by set algebras goes wrong in a sense. We present an algebraization F which is a variety and there is a nice representation by set algebras too (denote Crs* this class of set algebras). The axioms of F origin from the extended system (by the merry-go-round identities) of cylindrical axioms if the commutativity of cylindrifications (C4) is replaced by that of substitutions. We can prove that, similarly to the classical case, there is a class K of algebras such that an algebra A is representable (it is in ICrs*) if and only if A is a neat subreduct of an algebra in K with dimension large enough. Date received: July 7, 2004

25. List For KWIC List Of MSC2000 Phrases
algebras commutative rings and 13XX algebras composition 17A75 algebras cylindric and Polyadic algebras; relation 03G15 algebras De_Morgan algebras
http://www.math.unipd.it/~biblio/kwic/msc/m-kl_11_02.htm
algebras # categories of
algebras # chain conditions, complete
algebras # coalgebras, bialgebras, Hopf
algebras # cohomology of Lie (super)
algebras # color Lie (super)
algebras # commutative Banach algebras and commutative topological
algebras # commutative rings and 13-XX
algebras # composition
algebras # cylindric and polyadic algebras; relation
algebras # De_Morgan algebras, Lukasiewicz
algebras # decomposition theory for $C^*$- algebras # derivations, actions of Lie algebras # derivations, dissipations and positive semigroups in $C^*$- algebras # division algebras # division algebras # dual algebras; weakly closed singly generated operator algebras # dual spaces of operator algebras # exceptional (super) algebras # exterior algebra, Grassmann algebras # finitary algebras # finite rings and finite-dimensional algebras # flexible algebras # free algebras # free algebras # free probability and free operator algebras # functional calculus in topological algebras # general theory of $C^*$- algebras # general theory of commutative topological algebras # general theory of topological algebras # general theory of von_Neumann algebras # genetic algebras # graded Lie (super) algebras # Hermitian symmetric spaces, bounded symmetric domains Jordan

26. Gnist.no
Equality in Polyadic algebras; Terms and Equality Predicates, terms, operations, and equality in Polyadic Boolean algebras; Brief Summary Polyadic Boolean
http://www.gnist.no/vare.php?ean=9780821841389

27. Springer Online Reference Works
A related theory of Polyadic algebras, due to P.R. Halmos a5, emphasizes operators corresponding to the logical operation of substitution of terms for
http://eom.springer.de/b/b110750.htm

Encyclopaedia of Mathematics B
Article refers to
Boolean algebra with operators An operator on a Boolean algebra is a finitary operation on the Boolean algebra that is additive, meaning that in each of its arguments it preserves the sum/join operation of . An operator is normal if each argument preserves the least element of . Major examples of normal operators are as follows. Relation algebras : the algebra of binary relations on a set (i.e. the set of subsets of ) has the binary operator of composition of relations and the unary inverse operator . The axiomatic study of these operators quickly leads to deep questions about representability of equationally defined abstract algebras as concrete algebras of relations (cf. Cylindric algebras : on the algebra of subsets of a Cartesian product set , let be the operator assigning to each the cylinder generated by translating parallel to the -th coordinate axis. If is defined by a formula having variables , then the cylinder is defined by the existentially quantified formula . This observation leads to a comprehensive algebraic theory with many applications to quantificational logic . A related theory of polyadic algebras, due to

28. 03Gxx
03G05 Boolean algebras See also 06Exx; 03G10 Lattices and related structures See also 06Bxx 03G15 Cylindric and Polyadic algebras; relation algebras
http://www.ams.org/msc/03Gxx.html
Home MathSciNet Journals Books ...
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  • 03G05 Boolean algebras [See also 03G10 Lattices and related structures [See also 03G12 Quantum logic [See also 03G15 Cylindric and polyadic algebras; relation algebras 03G20 Lukasiewicz and Post algebras [See also 03G25 Other algebras related to logic [See also 03G30 Categorical logic, topoi [See also 03G99 None of the above, but in this section

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29. Salibra/papers.html
Polyadic algebras over nonclassical logics. D. Pigozzi and A. Salibra. Algebraic Methods in Logic and in Computer Science, C. Rauszer (ed.
http://www.dsi.unive.it/~salibra/papersnino.html
Antonino Salibra Papers 2000-2007
  • Applying Universal Algebra to Lambda Calculus.
    G. Manzonetto and A. Salibra.
    In preparation
  • Boolean algebras and lambda calculus.
    A. Salibra.
    International Conference on Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07), St Anne's College, University of Oxford, Oxford, England, August 5-9, 2007. Abstract(pdf) Slides(pdf)
  • Algebra and topology in lambda calculus.
    A. Salibra.
    Plenary Presentation at International Conference on Order, Algebra and Logics, Vanderbilt University, Nashville, USA, June 12-17, 2007. Abstract(pdf) Slides(pdf)
  • Lambda theories of effective lambda models.
    C. Berline, G. Manzonetto and A. Salibra.
    16th EACSL Annual Conference on Computer Science and Logic (CSL'07), 11-15 September 2007, Lausanne, Switzerland Paper(pdf)
  • Graph lambda theories.
    A. Bucciarelli and A. Salibra.
    Mathematical Structures in Computer Science 200? (to appear) Paper(pdf)
  • Boolean algebras for lambda calculus. G. Manzonetto and A. Salibra. 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), Seattle, Washington, Usa, August 12th-15th, 2006. Paper(pdf)
  • The sensible graph theories of lambda calculus.

30. The Book Pl@ce Title Detail
Equality in Polyadic algebras, Terms and Equality, Predicates, Terms, Operations, and Equality in Polyadic Boolean algebras, Brief Summary, Polyadic Boolean
http://www.bookplace.co.uk/bookplace/display.asp?K=9780821841389&aub=Paul Halmos

31. Back To Zentralblatt MATH Pages
03G15 Cylindric and Polyadic algebras, etc. 05A99 Classical combinatorial problems 11B83 Special sequences of integers and polynomials
http://www.zblmath.fiz-karlsruhe.de/MATH/general/erdos/cit/47303057.htm
Back to Zentralblatt MATH Pages
CD-ROM published
on the occasion of the
ICM 1998 in Berlin
Zentralblatt MATH
Zbl.No:
Autor:
Title: Sets of natural numbers of positive density and cylindric set algebras of dimension 2. (In English)
Source: Algebra Univers. 12, 81-92 (1981).
Review: Among others, the reported paper solves some fundamental problems of Ulam concerning projective algebras. To this, the paper uses and improves the theory of cylindric set algebras and their generalizations. Since the reported paper investigates structures treated systematically and extensively in the textbook by and Cylindric set algebras, Lect. Notes Math. 883 (1981; Zbl 497.03025 ) on cylindric-relativized set algebras and their generalizations, we shall use the notation and terminology of this book. To this book we shall refer as HMTAN.
The broadest generalization of cylindric set algebras of dimension -s) is the class Crs of cylindric-relativized set algebras, see Def. I.1.1 in HMTAN p.4. The reported paper introduces two special classes of Crs -s which we shall denote by Crs rc and Crs rcd . Definition: A Crs is said to be rectangular if its unit is a Cartesian product, that is if

32. List KWIC DDC And MSC Lexical Connection
algebras commutative rings and 13XX algebras composition 17A75 algebras cylindric and Polyadic algebras; relation 03G15
http://www.mi.imati.cnr.it/~alberto/dml_11_01.htm
algebraic numbers # PV-numbers and generalizations; other special
algebraic numbers; Galois module structure of rings of integers # integral representations related to
algebraic numbers; rings of algebraic integers
algebraic operations
algebraic or transcendental equations # nonlinear
algebraic properties of function spaces
algebraic sets # real
algebraic spaces, stacks) # generalizations (
algebraic specification # abstract data types;
algebraic structures
algebraic structures # fuzzy algebraic structures # relations with infinite-dimensional Lie algebras and other algebraic systems # general 08-XX algebraic systems # individual linear operators as elements of algebraic systems # representations of groups as automorphism groups of algebraic systems # topological and differentiable algebraic systems # topological representations of algebraic systems and their representations # other topological algebraic systems of matrices algebraic theorems) # polynomials: location of zeros ( algebraic theories), structure, and semantics # theories (e.g. algebraic theory algebraic theory of languages and automata algebraic theory of quadratic forms; Witt groups and rings

33. MSC 2000 : CC = Algebras
03G15 Cylindric and Polyadic algebras; relation algebras 06D72 Fuzzy lattices (soft algebras) and related topics Nouveau code MSC 2000
http://portail.mathdoc.fr/cgi-bin/msc2000.py?L=fr&T=Q&C=msc2000&CC=Algebras

34. Strong Amalgamation, Beck--Chevalley For Equivalence Relations And Interpolation
{2} F. Borceux, Handbook of Categorical Algebra, in Encyclopedia of {3} A. Daigneault, Freedom in Polyadic algebras and two theorems of Beth and Craig,
http://portal.acm.org/citation.cfm?id=937449

35. Matches For:
Homogeneous locally finite Polyadic Boolean algebras of infinite degree; Terms Algebraic logic, III. Predicates, terms, and operations in Polyadic algebras
http://www.jpbm.org/bookstore?fn=20&arg1=chelsealist&item=CHEL-154

36. Hajnal Andreka, Steven Givant, Szabolcs Mikulas, Istvan Nemeti
This theorem and its analogues for quasiPolyadic algebras with and without equality are formulated in the Henkin-Monk-Tarski monograph on cylindric
http://www2.renyi.hu/pub/algebraic-logic/rect.dense.abstract
Hajnal Andreka, Steven Givant, Szabolcs Mikulas, Istvan Nemeti, and Andras Simon NOTIONS OF DENSITY THAT IMPLY REPRESENTABILITY IN ALGEBRAIC LOGIC Abstract: Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable (as a cylindric set algebra). This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in the Henkin-Monk-Tarski monograph on cylindric algebras [HMT]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result to other classes of algebras of logic, for example quasi-polyadic algebras and substitution-cylindrification algebras with and without equality, relation algebras, and special Boolean monoids. The results of [HMT] mentioned above are special cases of our general theorems. We point out an error in the proof of the [HMT] representation theorem for atomic equality-free quasi-polyadic algebras with rectangular atoms. The error consists in the implicit assumption of a property that does not, in general, hold. We then give a correct proof of their theorem. Henkin and Tarski also introduced the notion of a rich cylindric algebra and proved in [HMT] that every rich cylindric algebra of finite dimension (or, more generally, of locally finite dimension) satisfying certain special identities is representable. We introduce a modification of the notion of a rich algebra that, in our opinion, renders it more natural. In particular, under this modification richness becomes a density notion. Moreover, our notion of richness applies not only to algebras with equality, but also to algebras without equality. We show that a finite dimensional algebra is rich iff it is rectangularly dense and quasi-atomic; moreover, each of these conditions is also equivalent to a very natural condition of point density. As a consequence, every finite dimensional (or locally finite dimensional) rich algebra of logic is representable. We do not have to assume the validity of any special identities to establish this representability. Not only does this give an improvement of the Henkin-Tarski representation theorem for rich cylindric algebras, it solves positively an open problem in [HMT] concerning the representability of finite dimensional rich quasi-polyadic algebras without equality.

37. LINGUIST List 18.3537: Studia Logica 87/1 (2007)
Finitary Polyadic algebras from Cylindric algebras DOI 10.1007/s11225007-9073-6 Autor Miklós Ferenczi A Duality for the algebras of a ukasiewicz n +
http://linguistlist.org/issues/18/18-3537.html
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Mon Nov 26 2007
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1. Jasper de Vaal, Studia Logica Vol 87, No 1 (2007)
Message 1: Studia Logica Vol 87, No 1 (2007) Date: 14-Nov-2007
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Publisher: Springer
http://www.springer.com Journal Title: Studia Logica Volume Number: 87 Issue Number: 1 Issue Date: 2007 Main Text: Finitary Polyadic Algebras from Cylindric Algebras DOI 10.1007/s11225-007-9073-6 Autor Mikl³s Ferenczi A Duality for the Algebras of a Łukasiewicz n + 1-valued Modal System DOI 10.1007/s11225-007-9074-5 Autor Bruno Teheux Second-Order Quantifier Elimination in Higher-Order Contexts with Applications to the Semantical Analysis of Conditionals DOI 10.1007/s11225-007-9075-4 Autoren Dov M. Gabbay und Andrzej Szałas Congruence Coherent Symmetric Extended de Morgan Algebras DOI 10.1007/s11225-007-9076-3 Autoren T. S. Blyth und Jie Fang The Insufficiency of the Dutch Book Argument DOI 10.1007/s11225-007-9077-2 Autor Darrell P. Rowbottom

38. PlanetMath:
03G05, , Boolean algebras. 03G10, -, Lattices and related structures. 03G12, -, Quantum logic. 03G15, -, Cylindric and Polyadic algebras; relation algebras
http://planetmath.org/browse/categories/03Gxx/
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Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Browsing MSC leaves only (Case insensitive substrings, use '-' to exclude) 03Gxx - Algebraic logic Boolean algebras Lattices and related structures Quantum logic Cylindric and polyadic algebras; relation algebras Lukasiewicz and Post algebras Other algebras related to logic Categorical logic, topoi Miscellaneous up top

39. 03Gxx
03G05 Boolean algebras See also 06Exx 03G10 Lattices and related Polyadic algebras; relation algebras 03G20 Lukasiewicz and Post algebras See also
http://www.emis.de/MSC2000/03Gxx.html
Algebraic logic 03G05 Boolean algebras [See also ] 03G10 Lattices and related structures [See also ] 03G12 Quantum logic [See also ] 03G15 Cylindric and polyadic algebras; relation algebras 03G20 Lukasiewicz and Post algebras [See also ] 03G25 Other algebras related to logic [See also ] 03G30 Categorical logic, topoi [See also ] 03G99 None of the above, but in this section
Version of December 15, 1998

40. PREDICATES, TERMS, OPERATIONS, AND EQUALITY IN POLYADIC BOOLEAN ALGEBRAS
PREDICATES, TERMS, OPERATIONS, AND EQUALITY IN Polyadic BOOLEAN algebras. Paul R. Halmos. DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CHICAGO. Full text
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=528233

41. 03Gxx
03G15, Cylindric and Polyadic algebras; relation algebras. 03G20, ukasiewicz and Post algebras See also 06D25, 06D30. 03G25, Other algebras related to
http://www.impan.gov.pl/MSC2000/03Gxx.html
Algebraic logic Boolean algebras
[See also Lattices and related structures
[See also Quantum logic
[See also Cylindric and polyadic algebras; relation algebras
[See also Other algebras related to logic
[See also Categorical logic, topoi
[See also None of the above, but in this section

42. Citebase - Algebraic Logic, Varieties Of Algebras And Algebraic Varieties
Diskin, Polyadic algebras for the nonclassical logics, Riga, Manuscript (1991), unpublished. G/A, 13 Z. Diskin, A unifying approach to algebraization of
http://www.citebase.org/abstract?identifier=oai:arXiv.org:math/0312420&action=ci

43. A Survey Of Abstract Algebraic Logic
In contrast to Boolean, cylindric, Polyadic, and Wajsberg algebras which were defined before the LindenbaumTarski method was first applied to generate them
http://www.mat.ub.es/~jmfont/docs/Survey.html
A Survey of Abstract Algebraic Logic
by Josep Maria Font, Ramon Jansana and Don Pigozzi
Studia Logica (Special Issue on Abstract Algebraic Logic, part II)
See the corrections at the bottom of this page.
Introduction
It was not until much later that logicians started to think about connections between these two ways of looking at logic. Tarski ([131]) gave the precise connection between Boolean algebra and the classical propositional calculus. His approach builds on Lindenbaum's idea of viewing the set of formulas as an algebra with operations induced by the logical connectives. Logical equivalence is a congruence relation on the formula algebra, and the associated quotient algebra turns out to be a free Boolean algebra. This is the so-called Lindenbaum-Tarski method Other logics not relaying on the (classical) notion of truth, like intuitionistic logic (centered on the notion of constructive mathematical proof) or multiple-valued logic, can also be approached from the two points of view, the equivalential and the assertional. And the connection between them, like in the predicate-logic case, can be complicated. For instance, when the Lindenbaum- Tarski method is applied to the infinite-valued logistic system of Lukasiewicz one gets not MV-algebras, but the so-called Wajsberg algebras. In contrast to Boolean, cylindric, polyadic, and Wajsberg algebras which were defined before the Lindenbaum-Tarski method was first applied to generate them from the appropriate assertional systems, Heyting algebras seem to be the first algebras of logic that were identified by applying the Lindenbaum-Tarski method to a known assertional system, namely the intuitionistic propositional calculus.

44. AUTHOR INDEX
A model theoretic characterization of complexity of theories, 190195 27/4. Non-Computability of the Equational Theory of Polyadic algebras, 155-164 30/3
http://www.filozof.uni.lodz.pl/bulletin/s.html
BULLETIN OF THE SECTION OF LOGIC Author Index
To find any word: author, title or key word; please, press "Ctrl-F".
S
SAAD S., Figallo A. V. and Ramon G.
iH-Propositional Calculus
SAARINEN, Esa
On the logic of perception sentences
SABALSKI, Bogdan
Some remarks about continuous Boolean algebras
SAGI, Gabor
A model theoretic characterization of complexity of theories
Non-Computability of the Equational Theory of Polyadic Algebras
SAGI, Gabor and Nemeti, Istvan and Madarasz, Judit
On the finitization problem of relational algebras
SAIN, Ildiko
Total correctness in nonstandard dynamic logic
Amalgamation, Epimorphisms and Definability Properties in Algebraic Logic
Computer sciences temporal logics need their clocks
On finitizing first order logic
SAIN, Ildiko and Nemeti, Istvan
Fork algebras in usual and in non-well-founded set theories. Part I
Fork algebras in usual and in non-well-founded set theories. Part II
SALONI, Zygmunt
The sequent Gentzen system for m-valued logic
SALTO, Francisco and Mendez, Jose
More on Peirce's law
SALTO, Francisco and Mendez, Jose and Robles, Gemma

45. Logic And Mathematics
That is an unfortunate misunderstanding cylindric algebras (and Polyadic algebras) were an important initial attempt in the 1950s to make explicit the
http://suo.ieee.org/email/msg12653.html
Thread Links Date Links Thread Prev Thread Next Thread Index Date Prev ... Date Index
logic and mathematics
Happy Bloomsday everyone, http://www.rejoycedublin2004.com/

46. Sachgebiete Der AMS-Klassifikation: 00-09
above but in this section 03Gxx Algebraic logic 03G05 Boolean algebras, Polyadic algebras; relation algebras 03G20 Lukasiewicz and Post algebras,
http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html
Sachgebiete der AMS-Klassifikation: 00-09
nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen
01-XX 03-XX 04-XX 05-XX 06-XX 08-XX
nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

47. MathNet-Mathematical Subject Classification
03G15, Cylindric and Polyadic algebras; relation algebras. 03G20, Lukasiewicz and Post algebras See also 06D25, 06D30. 03G25, Other algebras related to
http://basilo.kaist.ac.kr/API/?MIval=research_msc_out&class=03-XX

48. HeiDOK
03G15 Cylindric and Polyadic algebras; relation algebras ( 0 Dok. ) 03G20 Lukasiewicz and Post algebras ( 0 Dok. ) 03G25 Other algebras related to logic
http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03G&anzahl

49. Charles Pinter
MR0321735 (48 102) Pinter, Charles A simpler set of axioms for Polyadic algebras. Fund. Math. 79 (1973), no. 3, 223232. (Reviewer S. Comer) 02J15
http://charlespinter.com/
Charles Pinter
Contact: Bucknell University, Lewisburg, PA 17837, USA e-mail: cpinter@bucknell.edu Tel.: 1-570-524-0989 Vital Statistics: Born: Budapest, Hungary, March 5, 1937. Primary/Secondary schools: Lycée Regnault and Lycée St. Aulaire, Tangier, Morocco. Undergraduate: B.Sc. Columbia University, New York Terminal degree: Docteur-ès-Sciences (Doctorat d’Etat), University of Paris, France. Academic Positions: University of Maryland, instructor 1960-64. University of Malaya, Kuala Lumpur, Fulbright professor 1967-68. University of California, Berkeley, NSF postdoctoral fellow, 1970-72. Bucknell University, professor 1965-present. Scientific publications: Only reviewed and cited articles are listed. Pinter, Charles C. Combinatorial tableaux in isoperimetry. Coding, cryptography and combinatorics, Progr. Comput. Sci. Appl. Logic, 23, Birkhäuser, Basel , 2004. (Reviewer: Jason Douglas Rosenhouse) Pinter, Charles C. Complexity of network training for classes of neural networks. Algorithmic learning theory (Fukuoka, 1995), Lecture Notes in Comput.

50. Logic And Language Links - Polyadic Algebra
Polyadic algebra. This concept has currently no gloss. Polyadic algebra is a subtopic of algebraic logic. Polyadic algebra has currently no subtopics.
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51. Concrete Groups And Axiomatic Theories I | The N-Category Café
A Polyadic Boolean algebra (which here will simply be called a theory) is a covariant functor T Fin Bool such that for every f m n in Fin,
http://golem.ph.utexas.edu/category/2007/10/concrete_groups_and_axiomatic.html
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October 26, 2007
Concrete Groups and Axiomatic Theories I
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Guest post by Todd Trimble Geometric Representation Theory notes ): a theory involves types, predicates on types, and axioms on predicates. For example, in Euclidean geometry, the types might be geometric figures like point, line, etc.; the predicates would be formal relations between figures, such as incidence, or how two planes can be related to each other, and of course there are axioms these predicates are assumed to satisfy. X and also quantifiers algebraically For a familiar example of a predicate theory, consider the theory where the predicates are identified with finitary relations on a set

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