Mathematical Logic Quarterly 46 (4):505-516 (2000)

Abstract
In this paper we study the model theory of extensions of models of first-order Peano Arithmetic by means of the arithmetized completeness theorem 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
Keywords ω‐consistency  Reflection principles  Arithmetized completeness theorem  End‐extensions  Models of arithmetic
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DOI 10.1002/1521-3870(200010)46:4
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