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Martina Pfeifer

Pierre Touchard: Burden in exact sequences of abelian groups

Thursday, 24.10.2019 11:00 im Raum SR 1D

Mathematik und Informatik

In model theory, the burden is a notion of dimension for NTP2 structures, which form a relatively tame class of first order structures. Chernikov and Simon (2016) consider exact sequences of abelian groups A -> B -> C, and modulo the hypothesis that B/nB is finite for all integers n, they prove a quantifier elimination result. Then, they compute the burden in a particular case: if the burden of A and burden of C are equal to 1, so is the burden of A->B->C. However, the condition of finite classes modulo n is restrictive. For instance, it is known that abelian groups with finite classes modulo n are exactly the ones of burden 1 (Jahnke, Simon, Walsberg). Using a new quantifier elimination result of Aschenbrenner, Chernikov, Gehret and Ziegler, one can show in general that the burden of a pure exact sequence of abelian groups is given by the following formula: bdn(A->B->C) = max_n (bdn(A/nA) + bdn(nC)). I will present some examples and a sketch of the proof. I will also present some applications of this result.



Angelegt am Thursday, 17.10.2019 15:03 von Martina Pfeifer
Geändert am Thursday, 17.10.2019 15:03 von Martina Pfeifer
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