UIUC Dept. of Mathematics Seminar Calendar

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                                               31

Tuesday, December 8, 2009

Logic Seminar
1:00 pm in 345 Altgeld Hall, Tuesday, December 8, 2009

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Submitted by w-henson.

Jana Marikova (WIU)
O-minimal residue fields of o-minimal fields, II.
Abstract: Let R be an o-minimal field with a proper convex subring V, and let k be the corresponding residue field with residue map st: V \to k. We show that a certain first order axiom scheme in the language of (R,V) singles out exactly the structures (R,V) such that k_{ind}, the residue field with structure induced from R via st, is o-minimal. It has been shown in previous work that if (R,V) satisfies the above mentioned axiom scheme, then k_{ind} is o-minimal. The other direction is new and the proof uses a recent result by Shiota.