omega consistency

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• Gentzen's consistency proof — Gentzen s theoremIn 1936 Gerhard Gentzen proved the consistency of first order arithmetic using combinatorial methods. Gentzen s proof shows much more than merely that first order arithmetic is consistent. Gentzen showed that the consistency of… …   Wikipedia

• Ω-consistent theory — In mathematical logic, an ω consistent (or omega consistent, also called numerically segregativeW.V.O. Quine, Set Theory and its Logic ] ) theory is a theory (collection of sentences) that is not only (syntactically) consistent (that is, does not …   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

• George Boolos — Infobox Person name = George Boolos birth date = birth date|1940|9|4|mf=y birth place = New York, New York, U.S. death date = death date and age|1996|5|27|1940|9|4|mf=y death place = Cambridge, Massachusetts, U.S.George Stephen Boolos (September… …   Wikipedia

• George Boolos — George Stephen Boolos (4 de septiembre de 1940, Nueva York – 27 de mayo de 1996) fue un filósofo y estudioso de lógica matemática que enseñó en el Massachusetts Institute of Technology. Contenido 1 Vida 2 Trabajo 3 Véase también …   Wikipedia Español

• Rosser's trick — For the theorem about the sparseness of prime numbers, see Rosser s theorem. For a general introduction to the incompleteness theorems, see Gödel s incompleteness theorems. In mathematical logic, Rosser s trick is a method for proving Gödel s… …   Wikipedia

• logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

• Francisco Antônio Dória — Francisco Antônio de Moraes Accioli Dória (born 1945, Rio de Janeiro, Brazil) is a Brazilian mathematician, philosopher, and noted genealogist. Francisco Antônio Dória received his B.S. in Chemical Engineering from the Federal University at Rio… …   Wikipedia

• New Foundations — In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled New Foundations for …   Wikipedia

• Zermelo set theory — Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory. It bears certain differences from its descendants, which are not always understood, and are frequently misquoted. This article… …   Wikipedia

• Gauge anomaly — In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics usually a one loop diagram that invalidates the gauge symmetry of a quantum field theory; i.e. of a gauge theory. Anomalies in gauge… …   Wikipedia