Ernest Schimmerling

Mathematical logic seminar - March 23, 2004

Time: 12 - 1:30 p.m.

Room: Wean Hall 7220

Speaker: Chris Miller
Associate Professor
Department of Mathematics
Ohio State University

Title: Avoiding the projective hierarchy in expansions of the real field by sequences

Abstract: Consider an expansion of the field of real numbers by a set of real numbers {a_k: k in N} where a_k goes monotonically to +\infty as k goes to +\infty. We are interested in knowing when the expansion does not define the set of all natural numbers N. I will discuss some known results. For example, N is not definable if (log a_{k+1})/(log a_k) goes to +\infty (joint work with Harvey Friedman). On the other hand, N is definable if (log a_k)/k goes to 0 subject to some further regularity conditions. What happens in between these two extremes is more subtle, and only partially understood.

Organizer's note:     Lunch will be provided.