On Dimensions, Standard Part Maps, and p-Adically Closed Fields

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Studies in Logic, Vol. 13, No. 6 (2020): 41–62    PII: 1674-3202(2020)-06-0041-22

Ningyuan Yao

Abstract. The aim of this paper is to study the dimensions and standard part maps between the field of p-adic numbers image-20230908120053-1 and its elementary extension K in the language of rings Lr. We show that for any K-definable set image-20230908120326-2, image-20230908120348-3. Let V ⊆ K be convex hull of K over image-20230908120053-1, and st : V → image-20230908120053-1 be the standard part map. We show that for any K-definable function image-20230908120518-4, there is definable subset image-20230908120640-5 such that image-20230908120658-6 has no interior, and for all x ∈ D, either image-20230908120742-7 is constant, orimage-20230908120804-8. We also prove that image-20230908120825-9 for every definable X ⊆ Km.

 

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