Philosophy dictionary. Academic. 2011.
Gödel numbering for sequences — A Gödel numbering for sequences provides us an effective way to represent each finite sequence of natural numbers as a single natural number. Of course, the embedding is surely possible set theoretically, but the emphasis is on the effectiveness… … Wikipedia
Gödel number — In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well formed formula of some formal language a unique natural number called its Gödel number. The concept was first used by Kurt Gödel for the proof of his… … Wikipedia
Numbering (computability theory) — In computability theory a numbering is the assignment of natural numbers to a set of objects like rational numbers, graphs or words in some language. A numbering can be used to transfer the idea of computability and related concepts, which are… … Wikipedia
Proof sketch for Gödel's first incompleteness theorem — This article gives a sketch of a proof of Gödel s first incompleteness theorem. This theorem applies to any formal theory that satisfies certain technical hypotheses which are discussed as needed during the sketch. We will assume for the… … Wikipedia
Complete numbering — In computability theory complete numberings are generalizations of Gödel numbering first introduced by A.I. Mal tsev in 1963. They are studied because several important results like the Kleene s recursion theorem and Rice s theorem, which were… … Wikipedia
Cylindric numbering — In computability theory a cylindric numbering is a special kind of numbering first introduced by Yuri L. Ershov in 1973. If a numberings ν is reducible to μ then there exists a computable function f with . Usually f is not injective but if μ is a … Wikipedia
Constructible universe — Gödel universe redirects here. For Kurt Gödel s cosmological solution to the Einstein field equations, see Gödel metric. In mathematics, the constructible universe (or Gödel s constructible universe), denoted L, is a particular class of sets… … Wikipedia
On Formally Undecidable Propositions of Principia Mathematica and Related Systems — This article describes the publication details of a famous paper in mathematical logic. For information about the theorems proved in this paper, see Gödel s incompleteness theorems. Über formal unentscheidbare Sätze der Principia Mathematica und… … Wikipedia
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
List of mathematics articles (G) — NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… … Wikipedia
