Chris Miller
The Ohio State University
Title
Quasiminimality of some entire functions
Abstract
Given a (complex-) entire function f, the question arises as to whether the expansion of the complex field by f is quasiminimal (that is, every unary definable set is either countable or co-countable). Of course, by quantifier elimination, this is true if f is polynomial. It has been known that quasiminimality can fail if f is of more than one variable, but so far, there are no counterexamples known in one variable. The question was open for quite some time as to whether there are any *examples* of nonpolynomial f of one variable, though there were suspects. Recently, A. Dmitrieva (East Anglia) verified that a class of suspected examples are indeed examples. I will present the result along with history, context and significance (but not a proof).
