Kolokviální přednáška se konala ve středu 9. listopadu 2016, v 16:00 v posluchárně M1

Wieslaw Kubiś (Institute of Mathematics, Czech Academy of Sciences, Prague)

Generic objects and infinite games

Abstract:

Let F be a fixed class of `small' mathematical structures (e.g. finite graphs, finite-dimensional normed spaces, etc.) and assume that a notion of `embedding' has been defined so that we can say that one structure is an extension of another. We say that a structure is `big' if it can be build as the union (or, more formally, colimit) of a chain of embeddings in F. Fix a big structure U. We consider the following infinite game for two players: Player I chooses a structure S_0 from F. Player II responds by its extension S_1, again in F. Player I responds by an extension S_2 of S_1. And so on. We say that Player II wins if the union of the infinite chain of S_ns is isomorphic to U, otherwise Player I wins. We say that U is generic, if Player II has a winning strategy.

In the talk I will present examples of generic objects in several areas of mathematics. Further, I will show some of their basic properties and relations to the theory of universal homogeneous models.

Záznam přednášky ZDE