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On Models Constructed by Means of the Arithmetized Completeness Theorem
Author(s) -
Kaye Richard,
Kotlarski Henryk
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200010)46:4<505::aid-malq505>3.0.co;2-m
Subject(s) - peano axioms , mathematics , gödel's completeness theorem , completeness (order theory) , model theory , extension (predicate logic) , second order arithmetic , consistency (knowledge bases) , calculus (dental) , reflection (computer programming) , discrete mathematics , algebra over a field , pure mathematics , mathematical analysis , computer science , medicine , dentistry , programming language
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.