Pantelis Eleftheriou - Expansions of o-minimal structures which introduce no new smooth functions
|Starts:||15:00 20 Nov 2019|
|Ends:||16:00 20 Nov 2019|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Current University students|
Pantelis Eleftheriou joins us for the logic seminar.
We study expansions of o-minimal structures which preserve the tame geometric behavior on the class of all definable sets. Two main categories arise according to whether there are dense-codense or infinite discrete definable sets. The expansion (R, 2^Q) of the real field by all rational powers of 2 belongs to the first category. The expansion (R, 2^Z) of the real field by all integer powers of 2 belongs to the second category. In both cases we seek topological/analytical conditions that imply certain definable objects be R-definable. In the first structure, it is known that every open definable set is R-definable. In the second structure, we prove that every infinitely differentiable function with R-definable domain is R-definable. We do this in a general axiomatic framework which also allows R to be a reduct of a real closed field. This is joint work with A. Savatovsky.
Organisation: University of Konstanz
Travel and Contact Information
Frank Adams 1
Alan Turing Building