The uniformization property in hereditary finite superstructures (Q1288095)

A theory is called regular provided it is model-complete and decidable. The author proves that, for an arbitrary model \(M\) of a regular theory, a superstructure HF\((M)\), which is the admissible set of all hereditarily finite sets over \(M\), possesses the uniformization property if and only if \(M\) is a model with \(\Sigma\)-definable Skolem functions. As a corollary, he derives that this property is satisfied for hereditarily finite superstructures over the fields of reals and \(p\)-adic numbers.