Gödel's completeness theorem
id:
g-del-s-completeness-theorem-204-16261590
title:
Gödel's completeness theorem
text:
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements of T as axioms. One sometimes says this as "anything true in all models is provable". The completeness theorem makes
brand slug:
wiki
category slug:
encyclopedia
description:
Fundamental theorem in mathematical logic
original url:
https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem
date created:
2001-10-14T00:27:13Z
date modified:
2024-09-10T02:29:59Z
main entity:
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image:
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fields total:
13
integrity:
16