Online algebra seminar - April 15th, 1pm |
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We will continue online on Thursday, April 15th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:
Mark Kamsma
Independence Relations in Abstract Elementary Categories
Abstract: In Shelah's classification of first-order theories we classify theories using combinatorial properties. The most well-known class is that of stable theories, which are very well-behaved. Simple theories are more general, and then even more general are the NSOP_1 theories. We can characterise those classes by the existence of a certain independence relation. For example, in vector spaces such an independence relation comes from linear independence. Part of this characterisation is canonicity of the independence relation: there can be at most one nice enough independence relation in a theory. Lieberman, Rosický and Vasey proved canonicity of stable-like independence relations in accessible categories. Inspired by this we introduce the framework of AECats (abstract elementary categories) and prove canonicity for simple-like and NSOP_1-like independence relations. This way we reconstruct part of the hierarchy that we have for first-order theories, but now in the very general category-theoretic setting.
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Last Updated on Tuesday, 13 April 2021 08:34 |