Sentence examples for completeness theorem from inspiring English sources

Not surprisingly, the set of general predicate tautologies of each of these logics is Σ1-complete (due to completeness theorem).

This lemma is the main step missing from the various earlier attempts at the proof due to Löwenheim and Skolem, and, in the context of the completeness theorem for first order logic, renders the connection between syntax and semantics completely explicit.

We establish a completeness theorem.

Gödel's completeness theorem and its consequences: the Löwenheim-Skolem theorem and the compactness theorem.

A completeness theorem for Kleene algebras and the algebra of regular events.

Gödel's original proof of the completeness theorem is closely related to the second proof above.

The completeness theorem says that we have all the rules of proof we could ever have.

Hoare logic notes The source for today's lecture on Cook's relative completeness theorem for Hoare logic can be found here.

Syntax and semantics; deductive systems; completeness and compactness theorems; first order calculi; Godel's completeness theorem; basic model theory, Skolem functions; Skolem-Lowenheim theorems.

Given the completeness theorem, it follows that the task of deciding whether any sentence is a theorem of the predicate calculus is equivalent to that of deciding whether any sentence is valid or whether its negation is satisfiable.

The basic tools and results achieved in model theory—such as the Löwenheim-Skolem theorem, the completeness theorem of elementary logic, and Skolem's construction of nonstandard models of arithmetic were developed during the period from 1915 to 1933.