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Recursion theory — Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability… … Wikipedia
Alpha recursion theory — In recursion theory, the mathematical theory of computability, alpha recursion (often written α recursion) is a generalisation of recursion theory to subsets of admissible ordinals alpha. An admissible ordinal is closed under Sigma 1(L alpha)… … Wikipedia
Reduction (recursion theory) — In computability theory, many reducibility relations (also called reductions, reducibilities, and notions of reducibility) are studied. They are motivated by the question: given sets A and B of natural numbers, is it possible to effectively… … Wikipedia
Forcing (recursion theory) — Forcing in recursion theory is a modification of Paul Cohen s original set theoretic technique of forcing to deal with the effective concerns in recursion theory. Conceptually the two techniques are quite similar, in both one attempts to build… … Wikipedia
Index set (recursion theory) — In the field of recursion theory, index sets describe classes of partial recursive functions, specifically they give all indices of functions in that class according to a fixed enumeration of partial recursive functions (a Gödel… … Wikipedia
Recursion — Recursion, in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition. The term is also used more generally to describe a process of repeating objects in a self… … Wikipedia
Theory of computation — In theoretical computer science, the theory of computation is the branch that deals with whether and how efficiently problems can be solved on a model of computation, using an algorithm. The field is divided into three major branches: automata… … Wikipedia
Recursion (computer science) — Recursion in computer science is a way of thinking about and solving problems. It is, in fact, one of the central ideas of computer science. [cite book last = Epp first = Susanna title = Discrete Mathematics with Applications year=1995… … Wikipedia
Recursion theorem — can refer to: * The recursion theorem in set theory * Kleene s recursion theorem, also called the fixed point theorem, in computability theory … Wikipedia
Theory (mathematical logic) — This article is about theories in a formal language, as studied in mathematical logic. For other uses, see Theory (disambiguation). In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. Usually… … Wikipedia
