A definability theorem for first order logic

1997/06/12 by Butz, Carsten, Moerdijk, Ieke
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.math/9706206

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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