An example of a $P$-minimal structure without definable Skolem functions
  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. 
Pablo Cubides Kovacsics and Kien Huu Nguyen
math.LO math.NT