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arXiv · 1905.11059

Pro-definability of spaces of definable types

Pablo Cubides Kovacsics·Jinhe Ye
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Abstract

We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued fields and closed ordered differential fields. Furthermore, we prove pro-definability of other distinguished subspaces, some of which have an interesting geometric interpretation. Our general strategy consists in showing that definable types are uniformly definable, a property which implies pro-definability using an argument due to E. Hrushovski and F. Loeser. Uniform definability of definable types is finally achieved by studying classes of stably embedded pairs.

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BibTeXRIS

Pablo Cubides Kovacsics, Jinhe Ye. 2019-05-27. Pro-definability of spaces of definable types. https://doi.org/10.1090/bproc%2F85

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