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Definability of types and VC density in differential topological fields

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Abstract

Given a model-complete theory of topological fields, we considered its generic differential expansions and under a certain hypothesis of largeness, we axiomatised the class of existentially closed ones. Here we show that a density result for definable types over definably closed subsets in such differential topological fields. Then we show two transfer results, one on the VC-density and the other one, on the combinatorial property NTP2.

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Acknowledgements

We would like to thank the referee for his detailed reading, his useful (and numerous) remarks. We also would like to thank Zoé Chatzidakis for having drawn our attention to the Kolchin polynomials and Pablo Cubidès for discussing the cell decomposition theorem.

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  1. Département de Mathématique, Université de Mons, Le Pentagone, 20, Place du Parc, 7000, Mons, Belgium

    Françoise Point

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  1. Françoise Point
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Correspondence to Françoise Point.

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Research Director at the “Fonds de la Recherche Scientifique (F.R.S.-F.N.R.S.)”.

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Point, F. Definability of types and VC density in differential topological fields. Arch. Math. Logic 57, 809–828 (2018). https://doi.org/10.1007/s00153-017-0607-y

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