An abstract setting for Henkin proofs

Topoi 3 (1):37-41 (1984)
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Abstract

A general result is proved about the existence of maximally consistent theories satisfying prescribed closure conditions. The principle is then used to give streamlined proofs of completeness and omitting-types theorems, in which inductive Henkin-style constructions are replaced by a demonstration that a certain theory respects a certain class of inference rules.

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Citations of this work

Varieties of complex algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
Forcing in proof theory.Jeremy Avigad - 2004 - Bulletin of Symbolic Logic 10 (3):305-333.
Quasi-apartness and neighbourhood spaces.Hajime Ishihara, Ray Mines, Peter Schuster & Luminiţa Vîţă - 2006 - Annals of Pure and Applied Logic 141 (1):296-306.

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References found in this work

The completeness of the first-order functional calculus.Leon Henkin - 1949 - Journal of Symbolic Logic 14 (3):159-166.
Admissible Sets and Structures.Jon Barwise - 1978 - Studia Logica 37 (3):297-299.
Saturated model theory.Gerald E. Sacks - 1972 - Reading, Mass.,: W. A. Benjamin.

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