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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Topologia i T. Mnogości

 

"An introduction to abstract Fraïssé theory" and "Uncountable homogeneous structures"


Prelegent: Adam Bartoš ("An introduction to abstract Fraïssé theory") and Wiesław Kubiś ("Uncountable homogeneous structures")

2023-12-06 16:15

"An introduction to abstract Fraïssé theory":

We give a gentle introduction to abstract countable discrete Fraïssé theory. First, we recall three classical examples of ultrahomogeneous structures: the linear order of the rationals, the random graph, and the Urysohn metric space, and we demonstrate the notions of ultrahomogeneity and injectivity on them. Then we recall the language and basic notions from category theory, and we formulate an abstract framework for building homogeneous structures. Finally, we argue the benefits of the framework – it covers both the classical model-theoretic countable Fraïssé limits as well as projective Fraïssé limits introduced by Irwin and Solecki.

 

"Uncountable homogeneous structures":

A first-order structure is said to be homogeneous if every isomorphism between its finitely generated substructures extends to an automorphism. We shall survey some well-known and some relatively new results and methods of building uncountable homogeneous structures.

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Nagrania obu odczytów można znaleźć pod tym linkiem:

https://drive.google.com/drive/folders/1hgFP5M9wWnr0i317ILfQdZYUD9VsfOeg?usp=sharing