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A definability theorem for first order logic

Carsten Butz·Ieke Moerdijk
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Abstract

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order formula. Our presentation is entirely selfcontained, and only requires familiarity with the most elementary properties of model theory.

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BibTeXRIS

Carsten Butz, Ieke Moerdijk. 1997-06-12. A definability theorem for first order logic. https://arxiv.org/abs/math/9706206

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