Title: Component-closed expansions of the real line (preliminary report)
Speaker: Chris Miller (Ohio State Univerity)
Abstract: While thinking about some problems in real-analytic geometry last year, Athipat Thamrongthanyalak (my now-former ZAP) and I stumbled across an intriguing, but considerably more basic, question: What can be said about first-order structures on the set of real numbers having the property that all connected components of definable sets are definable? And what can said about elementarily equivalent structures? We quickly found out that this question appears to be rather intimidating when stated over the field of reals, so we decided to first consider some toy models. I will describe the general plan, and discuss some of our progress.
