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2000•Mathematical logic quarterlyRequires access

On Models Constructed by Means of the Arithmetized Completeness Theorem

Richard Kaye, Henryk Kotlarski

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Abstract

In this paper we study the model theory of extensions of models of first-order Peano Arithmetic (PA) by means of the arithmetized completeness theorem (ACT) applied to a definable complete extension of PA in the original model. This leads us to many interesting model theoretic properties equivalent to reflection principles and ω-consistency, and these properties together with the associated first-order schemes extending PA are studied.

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What this paper is about

In this paper we study the model theory of extensions of models of first-order Peano Arithmetic (PA) by means of the arithmetized completeness theorem (ACT) applied to a definable complete extension of PA in the original model. This leads us to many interesting model theoretic properties equivalent to reflection principles and ω-consistency, and these properties together with the associated first-order schemes extending PA are studied.

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Available abstract

In this paper we study the model theory of extensions of models of first-order Peano Arithmetic (PA) by means of the arithmetized completeness theorem (ACT) applied to a definable complete extension of PA in the original model. This leads us to many interesting model theoretic properties equivalent to reflection principles and ω-consistency, and these properties together with the associated first-order schemes extending PA are studied.

Key concepts: Peano axioms, Mathematics, Gödel's completeness theorem, Completeness (order theory), Model theory, Extension (predicate logic), Second-order arithmetic, Consistency (knowledge bases)

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