Pantelis Eleftheriou - Expansions of o-minimal structures which introduce no new smooth functions
| Dates: | 20 November 2019 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Pantelis Eleftheriou |
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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.
Speaker
Pantelis Eleftheriou
Organisation: University of Konstanz
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Frank Adams 1
Alan Turing Building
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