Logic Seminar
Clifton Ealy, Jana Marikova, Chris Miller
details: http://www.math.uic.edu/~alice/mwmtday.html
MidWest Model Theory Day.
Abstract: Clifton Ealy: Thorn-Forking in Continuous Logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. We also obtain a new fact for classical real rosy theories: a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries. (Joint work with Isaac Goldbring.)
Jana Marikova: Valuations on o-minimal fields. Let R be an o-minimal field and V a proper convex subring. We show that the o-minimality of the corresponding residue field with structure induced from R via the residue map is equivalent to (R,V) satisfying a first-order axiom scheme.
Chris Miller: A continuous extension property for o-minimal expansions of ordered groups. Let $f:R^n \rightarrow R$ be bounded and definable in an o-minimal expansion of an ordered group R. Then there are finitely many cells $C_i$ in $R^n$ whose union has interior and the frontier of each $C_i$ contains the origin and $f$ extends continuously to the closure of $C_i$. This gives an open set U of real numbers such that the expansion of the real exponential field by U Borel-interprets the real projective hierarchy, yet every definable set either has interior or is nowhere dense.
Lunch at 11 at Joy Yee's (1335 S. Halsted).
Talks at 1pm, 2:30pm, 4pm in the order listed above.
Dinner at 5:30pm at the Parthenon (314 S Halsted St)
Tuesday February 16, 2010 at 11:00 AM in SEO 636