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1. PlanetMath: Recursively Enumerable Object id is 3045, canonical name is Recursivelyenumerable. Computability and recursion theory Recursively enumerable sets and degrees) http://planetmath.org/encyclopedia/RecursivelyEnumerable.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About recursively enumerable (Definition) For a language TFAE There exists a Turing machine such that terminates There exists a total recursive function which is onto There exists a total recursive function which is one-to-one and onto A language fulfilling any (and therefore all ) of the above conditions is called recursively enumerable Examples Any recursive language. The set of encodings of Turing machines which halt when given no input. The set of encodings of theorems of Peano arithmetic The set of integers for which the hailstone sequence starting at reaches 1. (We don't know if this set is recursive, or even if it is ; but a trivial program shows it is recursively enumerable.) "recursively enumerable" is owned by ariels view preamble View style: HTML with images page images TeX source See Also: halting problem Turing computable Other names: semi-recursive Also defines: semi-recursive, recursively enumerable function

2. Signatures From EmilPost Post is best known for his work on polyadic groups, Recursivelyenumerable sets, and degrees of unsolvability, as well as for his contribution to the http://c2.com/cgi/wikiSig?EmilPost

3. $d$-simple Sets, Small Sets, And Degree Classes. 22 C. E. M. Yates, Three theorems on the degree of Recursivelyenumerable sets, Duke Math. J., 32 (1965),461468. Mathematical Reviews (MathSciNet) MR31 http://projecteuclid.org/handle/euclid.pjm/1102780321

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next $d$-simple sets, small sets, and degree classes. Manuel Lerman and Robert I. Soare Source: Pacific J. Math. Volume 87, Number 1 (1980), 135-155. Primary Subjects: Secondary Subjects: Full-text: Access granted (open access) PDF File (2151 KB) DjVu File (485 KB) Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102780321 Zentralblatt Math identifier: Mathematical Reviews number (MathSciNet): back to Table of Contents References [1] V. L. Bennison and R. I. Soare, Some lowness propertiesand computational com- plexity sequences, Theoretical Computer Science, 6 (1978),233-254. Mathematical Reviews (MathSciNet): Zentralblatt MATH: [2] A. H. Lachlan, On the lattice of recursively enumerable sets, Trans. Amer. Math. Soc, 130 (1968), 1-37. Mathematical Reviews (MathSciNet): Zentralblatt MATH: [3] A. H. Lachlan,The elementary theory of recursively enumerable sets, Duke Math. J., 35 (1968), 123-146.

4. JSTOR Degree Theoretic Definitions Of The Low$_2$ Recursively There exist low2lowl wtt-bottomed T-degrees containing r. e. sets of 1993 , Working below a high Recursivelyenumerable degree, this JOURNAL, http://links.jstor.org/sici?sici=0022-4812(199509)60:3<727:DTDOTL>2.0.CO;2-6

5. Post's Theorem the connection between the arithmetical hierarchy and the Turing degrees . For every , if and only if and only if B is a Recursivelyenumerable set http://www.therfcc.org/post's-theorem-357961.html

Post's theorem In mathematics Post's theorem in recursion theory describes the connection between the arithmetical hierarchy and the Turing degrees . As notation we say that a subset X of is n if there is a n formula with free variable n which is true if andonly if n is in X Formally Post's theorem states: For every if and only if and only if B is a recursivelyenumerable set with an oracle of some n set or, equivalently, some n set. , i.e. the n -th Turing jump of the empty set is n complete for every n if and only if , i.e. B is Turing reducible to The first result says that the n sets represent sets which are computablyenumerable with an oracle in a one lower set. The second results says that the Turing jumps form complete sets of the n X complete for n means that every other set in n is Turing reducible from X As immediate corollaries we get: if and only if B is a recursivelyenumerable set with an oracle of if and only if , i.e. B isTuring reducible to The result is named for Emil Post Other Languages: Danish Dutch English French ... Swedish This article originally from Wikipedia. The text on this site is made available under the terms of the GNU Free Documentation Licence Partner Sites: Anoca Encyclopedia Google Yahoo

6. Wiki Blog Translate this page (Recursivelyenumerable). .. JavaSwf 2 is a set of Java packages that enable the parsing, http://jania.pe.kr/wiki/jwiki/moin.cgi/WikiBlog

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