National Institute of the Republic of Serbia

ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζωῶν τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

**THE NOVI SAD Seminar**

**PROGRAM**

**Plan rada Novosadskog seminara za FEBRUAR 2024.**

Registracija za učešće na seminaru je dostupna na sledećem linku:

https://miteam.mi.sanu.ac.rs/asset/Xqhz2H88SoxmX53xw

Ukoliko ste već registrovani predavanje možete pratiti na sledećem linku (nakon sto se ulogujete):

https://miteam.mi.sanu.ac.rs/asset/den7QsS2NK8N8oHwQ

Neulogovani korisnici mogu pratiti prenos predavanja na ovom linku (ali ne mogu postavljati pitanja osim putem chata i ne ulaze u evidenciju prisustva):

https://miteam.mi.sanu.ac.rs/call/den7QsS2NK8N8oHwQ/mEOVHCS6ddid6VfVLgrXxcDb0A2IoJ2Ln5_c7pVQw9J

Fraı̈ssé’s theorem is concerned with the existence of highly symmetric structures that are universal for a given class of finitely generated structures, so called universal homogeneous structures (or Fraı̈ssé-limits). Prominent examples include the Rado graph (a.k.a. the countable random graph), the (rational) Urysohn space, the rationals…

At the center of Fraı̈ssé theory stands the notion of an age. Every age is equal the isomorphism-closure of the class of finitely generated substructures of a given countable structure.

For any age C the class σC of countable structures younger than C may be obtained by closing C for certain direct limits of ω-sequences of structures from C. Fraı̈ssé-limits live in classes of the shape σC, where C is an age that has the amalgamation property.

During this talk I will shed some light on the constructive power of the dual of this construction—projective limits of dual ω-sequences of structures. It turns out that limits of dual ω-sequences give rise to certain metric structures. The class of metric structures obtainable in this way from a given class C of structures is denoted by πC.

I will present the answer to the question when for a given age C the class πσC contains a universal homogeneous metric structure. Here a metric structure is called homogeneous if every metric isomorphism between profinitely generated substructures is extendable to a metric automorphism of the structure in question.

This is joint work with Wiesław Kubiś and Maja Pech.

Marko Janev

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Anastazia Žunić

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