# Search results

- ...the basis of which lies a certain synthesis of ideas in the theory of sets and algorithms (see [[#References|[2]]]). ...TD valign="top">[2]</TD> <TD valign="top"> J. Barwise, "Admissible sets and structures" , Springer (1975)</TD></TR></table>1 KB (150 words) - 17:27, 7 February 2011
- $#C+1 = 7 : ~/encyclopedia/old_files/data/M065/M.0605390 Multiple recursion Please remove this comment and the {{TEX|auto}} line below,2 KB (313 words) - 08:02, 6 June 2020
- ...ained by primitive recursion from an $n$-place function $g(x_1,\dots,x_n)$ and an $(n+2)$-place function $h(x_1,\dots,x_n,y,z)$ if for all natural number and2 KB (371 words) - 21:13, 2 November 2014
- ...ly enumerable. Many sets playing an important role in recursive set theory and its applications are productive (e.g. the set of all Gödel numbers of gene ...lign="top"> H. Rogers jr., "Theory of recursive functions and effective computability" , McGraw-Hill (1967) pp. 164–165</TD></TR></table>2 KB (288 words) - 17:33, 15 November 2014
- ...re of interest from the point of the view of the recursive analogue of the theory of [[cardinal number]]s. In [[recursive set theory]] and its applications one also uses certain special subclasses of the class of i1 KB (194 words) - 11:14, 3 September 2017
- <TR><TD valign="top">[2]</TD> <TD valign="top"> A.I. Mal'tsev, "Algorithms and recursive functions" , Wolters-Noordhoff (1970) (Translated from Russian)2 KB (253 words) - 12:32, 17 January 2016
- ...t]]; in other words, a set $A$ is creative if it is recursively enumerable and if there exists a [[partial recursive function]] $\phi(x)$ such that, for a ...numerable sets. The concept of creativity generalizes to sequences of sets and other objects.2 KB (295 words) - 06:52, 28 September 2016
- $#C+1 = 86 : ~/encyclopedia/old_files/data/R080/R.0800210 Recursion Please remove this comment and the {{TEX|auto}} line below,13 KB (2,044 words) - 08:10, 6 June 2020
- Please remove this comment and the {{TEX|auto}} line below, ...umber of the operations of composition and [[Primitive recursion|primitive recursion]].6 KB (843 words) - 08:07, 6 June 2020
- Please remove this comment and the {{TEX|auto}} line below, A method used in [[Recursion|recursion]] theory for the construction of sets with a simple structure (from the recursive po3 KB (488 words) - 08:07, 6 June 2020
- ...lign="top"> H. Rogers jr., "Theory of recursive functions and effective computability" , McGraw-Hill (1967) pp. 164–165</TD></TR> ...tin, "Bounded Queries in Recursion Theory", Progress in Computer Science and Applied Logic '''16'''. Springer (1999) ISBN 0817639667</TD></TR>2 KB (297 words) - 22:37, 10 January 2016
- Please remove this comment and the {{TEX|auto}} line below, ...], defined as follows. One examines functions given on the natural numbers and with natural values. The functions are assumed to be partial, i.e. they are5 KB (720 words) - 08:10, 6 June 2020
- ...duction (see below). It subsumes addition, multiplication, exponentiation, and all higher-order analogues of these operations. Because of this it grows to ...ermitted in primitive recursion fail to capture completely the notion of "computability" (cf. also [[Computable function|Computable function]]); one needs to perm10 KB (1,437 words) - 17:27, 7 February 2011
- ..., by its table; the number of arguments of the function may depend on $a$) and numbers $b_1,\ldots,b_n$ such that $a\in A$ is equivalent to the truth of $ ...quivalence relation $\equiv_{tt}$, namely $A\equiv_{tt}B$ if $A\leq_{tt}B$ and $B\leq_{tt}A$. The equivalence classes for this relation are called truth-t3 KB (414 words) - 21:57, 16 January 2016
- Please remove this comment and the {{TEX|auto}} line below, ...of the simpler classes. The most important hierarchies in descriptive set theory are defined as follows. If $ T $9 KB (1,244 words) - 22:10, 5 June 2020
- where the $R_i$ and $R$ are atomic formulas (and $R$ could also be $x_p = x_q$ or $\texttt{false}$. (Strict) propositional H ...exttt{false}$. In the strict case $q = \texttt{false}$ is excluded. A Horn theory is a set of Horn clauses.7 KB (1,111 words) - 06:59, 21 October 2016
- $#C+1 = 130 : ~/encyclopedia/old_files/data/R080/R.0800340 Recursive set theory Please remove this comment and the {{TEX|auto}} line below,16 KB (2,323 words) - 08:10, 6 June 2020
- Please remove this comment and the {{TEX|auto}} line below, ...ed his machines (cf. [[Turing machine]]) and showed that Turing computable and lambda definable are equivalent notions. These are arguments for the Church15 KB (2,326 words) - 22:15, 5 June 2020
- Please remove this comment and the {{TEX|auto}} line below, ...m for the solution of a given infinite series of problems of a given type, and of finding such an algorithm if it exists.21 KB (3,278 words) - 16:10, 1 April 2020