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recursively creative set

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  • Recursively enumerable set — In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing recognizable if: There is an algorithm such that the set of… …   Wikipedia

  • Creative and productive sets — In computability theory, productive sets and creative sets are types of sets of natural numbers that have important applications in mathematical logic. They are a standard topic in mathematical logic textbooks such as Soare (1987) and Rogers… …   Wikipedia

  • set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

  • Simple set — In recursion theory a simple set is an example of a set which is recursively enumerable but not recursive. Definition A subset S of the natural numbers N is called simple if it satisfies the following properties # N S is infinite and contains no… …   Wikipedia

  • 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

  • Computability theory — For the concept of computability, see Computability. Computability theory, also called recursion 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 …   Wikipedia

  • RE (complexity) — In computability theory and computational complexity theory, RE (recursively enumerable) is the class of decision problems for which a yes answer can be verified by a Turing machine in a finite amount of time.[1] Informally, it means that if the… …   Wikipedia

  • RE-complete — is the set of decision problems that are complete for the complexity class RE consisting of all recursively enumerable problems. In a sense, these are the hardest recursively enumerable problems. All such problems are nonrecursive. Generally, no… …   Wikipedia

  • Theory — The word theory has many distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion.In science a theory is a testable model of the manner of interaction of a set of natural phenomena,… …   Wikipedia

  • Axiom — This article is about logical propositions. For other uses, see Axiom (disambiguation). In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered either to be self evident or to define and… …   Wikipedia

  • List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

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