# 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 and 2 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 i 1 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 setA$is creative if it is recursively enumerable and if there exists a [[partial recursive function]]$\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 (887 words) - 14:54, 7 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 po
3 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 are
5 KB (735 words) - 14:55, 7 June 2020
• ..., 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$. The equivalence classes for this relation are called truth-t 3 KB (414 words) - 21:57, 16 January 2016 • Please remove this comment and the {{TEX|auto}} line below, ...of the simpler classes. The most important hierarchies in descriptive set theory are defined as follows. If$ T $9 KB (1,244 words) - 22:10, 5 June 2020 • If the TeX and formula formatting is correct, please remove this message and the {{TEX|semi-auto}} category. ...duction (see below). It subsumes addition, multiplication, exponentiation, and all higher-order analogues of these operations. Because of this it grows to 7 KB (994 words) - 16:46, 1 July 2020 • where the$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
• If the TeX and formula formatting is correct, please remove this message and the {{TEX|semi-auto}} category. ...ed his machines (cf. [[Turing machine]]) and showed that Turing computable and lambda definable are equivalent notions. These are arguments for the Church
15 KB (2,306 words) - 16:57, 1 July 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