Logic Seminar
Chris Miller
Ohio State
Expanding the real field by entire, and related, functions
Abstract: Let f be an entire function of one complex variable, regarded as a map from R^2
to R^2. It is known that the expansion of the real field (R,+,x) by all
restrictions of f to compact balls is o-minimal, and similarly for all
restrictions of the maximum function M_f(r):=max{|f(z)|:|z|=r}, r>0.
Preliminary investigation suggests that, under any "reasonable" assumptions,
(R,+,x,f) defines the set of all integers. On the other hand, the situation
regarding M_f is quite unclear. In particular, I have no examples where I know
that (R,+,x,M_f) is not o-minimal (though surely some must exist). I will
illustrate the issues by examining the case that f is defined by an Euler
partition product.
Tuesday September 11, 2007 at 4:00 PM in SEO 427