Abstract:
Given a polynomially bounded structure S that defines restricted power functions, we prove that a all intermediate structures between S and the expansion S^IR of S by all real power functions are of the form S^L where L is an intermediate field between IR and the field of exponents of S. This result can be understood as a polynomially bounded version of a conjecture of van den Dries and Miller. (Joint work with Gareth Jones, Manchester).