Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability...

The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories....

Gödel's theorem may refer to any of several theorems developed by the mathematician Kurt Gödel: Gödel's incompleteness theorems Gödel's completeness theorem...

Dedekind, and Georg Cantor. Gödel's discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929 as part of his dissertation...

despite the incompleteness theorem, by finding suitable further axioms to add to set theory. Gödel's completeness theorem establishes an equivalence in...

¬φ is a theorem of S. Syntactical completeness is a stronger property than semantic completeness. If a formal system is syntactically complete, a corresponding...

provable theorems (for an appropriate sense of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness. Complete theories...

theorem – Measure of algorithmic complexityPages displaying short descriptions of redirect targets Gödel's completeness theorem – Fundamental theorem...

Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development...

Estimation of covariance matrices Fermat's little theorem and some proofs Gödel's completeness theorem and its original proof Mathematical induction and...

undecidable in the theory used to describe the model. For example, by Gödel's incompleteness theorem, we know that any consistent theory whose axioms are true for...

sentences, the compactness theorem follows. In fact, the compactness theorem is equivalent to Gödel's completeness theorem, and both are equivalent to...

it is co-recursively enumerable). Trakhtenbrot's theorem implies that Gödel's completeness theorem (that is fundamental to first-order logic) does not...

encoding Description number Gödel numbering for sequences Gödel's incompleteness theorems Chaitin's incompleteness theorem Gödel's notation: 176  has been...

proofs of systems such as Peano arithmetic. Gödel's completeness theorem states that first-order logic is complete. Metamathematics Use–mention distinction...

Soundness theorem Gödel's completeness theorem Original proof of Gödel's completeness theorem Compactness theorem Löwenheim–Skolem theorem Skolem's paradox...

discovery - a proof of Kurt Gödel's Gödel's completeness theorem for full predicate logic with identity and function symbols. Gödel's proof of 1930 for predicate...

equivalent to consistency for first-order logic, a result known as Gödel's completeness theorem. The negation of satisfiability is unsatisfiability, and the...

structure. It's a consequence of Gödel's completeness theorem (not to be confused with his incompleteness theorems) that a theory has a model if and...

Gödel's construction, see Gödel 1940, pp. 35–46 or Cohen 1966, pp. 99–103. Cohen also gave a detailed proof of Gödel's relative consistency theorems using...

sometimes called the theorems of the system, especially in the context of first-order logic where Gödel's completeness theorem establishes the equivalence...

sentence from the axioms. The compactness theorem first appeared as a lemma in Gödel's proof of the completeness theorem, and it took many years before logicians...

sort. For his axiomatisation, Henkin proved that Gödel's completeness theorem and compactness theorem, which hold for first-order logic, carry over to...

structures under finite model theory include the compactness theorem, Gödel's completeness theorem, and the method of ultraproducts for first-order logic (FO)...

logic, providing a more practical method than one following from Gödel's completeness theorem. The resolution rule can be traced back to Davis and Putnam (1960);...

completeness axiom. In the 1930s, Kurt Gödel and Gerhard Gentzen proved results that cast new light on the problem. Some feel that Gödel's theorems give...

by Kurt Gödel in 1930 to be enough to produce every theorem. The actual notion of computation was isolated soon after, starting with Gödel's incompleteness...

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...

In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L , {\displaystyle L,} is a particular class...