Další seminář z algebry se koná 15.4.2021 od 13.00 online na platformě ZOOM. Informace pro připojení a další program semináře je zde. Mark Kamsma
Independence Relations in Abstract Elementary Categories
Abstrakt: In Shelah's classification of firstorder theories we classify theories using combinatorial properties. The most wellknown class is that of stable theories, which are very wellbehaved. 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 stablelike independence relations in accessible categories. Inspired by this we introduce the framework of AECats (abstract elementary categories) and prove canonicity for simplelike and NSOP_1like independence relations. This way we reconstruct part of the hierarchy that we have for firstorder theories, but now in the very general categorytheoretic setting.
