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.
