An example of a $P$-minimal structure without definable Skolem functions

20 Mar 2018 · Kovacsics Pablo Cubides, Nguyen Kien Huu ·

We show there are intermediate $P$-minimal structures between the semi-algebraic and sub-analytic languages which do not have definable Skolem functions. As a consequence, by a result of Mourgues, this shows there are $P$-minimal structures which do not admit classical cell decomposition.