Title: Uniformization Property in Heredidary Finite Superstructures

Abstract: In this article, we consider admissible sets of kind $HF({\mathfrak M})$, where ${\mathfrak M}$ is a model of a regular theory. We find a criterion of uniformization in $HF({\mathfrak M})$ formulated in terms of definability of Skolem functions. As a corollary, we prove that hereditary finite superstructures over reals and over p-adic numbers have the uniformization property.

PDF