Blog Archives

Topic Archive: o-minimality

Model theory seminarFriday, March 6, 201512:30 pmGC 6417

Alf Dolich

Generic Linear Functions over Divisible Ordered Abelian Groups

The City University of New York

Let T be the theory of divisible ordered Abelian groups in a language L
where T has quantifier elimination. Let f be a new unary function symbol. We
would like to consider the L(f)-theory T(a) expanding T together with axioms
for “f is an automorphism”. Unfortunately it is well known that T(a) does not
have a model companion and generally is not easy to analyze. Rather we look at
a weaker theory T(l) once again expanding T but with axioms for “l is a linear
bijection”. T(l) has a model companion and we provide a detailed analysis of
this theory.

Model theory seminarFriday, March 20, 201512:30 pmGC 6417

Whitney’s Extension Theorem in O-minimal Context

Ohio State University

Let $U$ be an open subset of $R^n$ and $f$, a function from $U$ to $R$, be $C^m$. We call the collection of $f$ and its derivatives, the jet of order $m$ of $f$. In 1934, H. Whitney asked how can we determine whether a collection of continuous functions on a closed subset of $R^n$ is a jet of order $m$ of a $C^m$-function and also gave a solution to this question which is known as Whitney’s Extension Theorem.
In this talk, let $R$ be an o-minimal expansion of the real field. We discuss whether a collection of continuous functions on a closed subset of $R^n$ is a jet of order $m$ of a $C^m$-function which is definable in $R$.

University of Toronto
Alex Rennet is a postdoc in the Mathematics department at the University of Toronto working under the supervision of Bill Weiss. His research focus right now is in o-minimality and in particular, ultraproducts of o-minimal structures. He received his Ph.D. in 2012 at the University of California at Berkeley, under the supervision of Thomas Scanlon.
Alf Dolich
The City University of New York
Professor Dolich (Ph.D. 2002 University of Maryland, M.A. Columbia University, B.A. University of Pennsylvania) held a VIGRE Van Vleck Assistant Professorship at the University of Wisconsin, Madison, before coming to the New York area, where he now holds an Assistant Professor position at Kingsborough CC of CUNY. Professor Dolich conducts research in model theory, simple theories, and o-minimal theories with secondary interests in algebraic geometry and set theory.