Seminar in set theory, set-theoretic topology, and model theory


Talks are on Tuesdays at 10:15 CET either at the Department of Mathematics and Informatics or online. This depends on the speaker and the epidemiological situation.
Main topics of the seminar are set theory, topology, model theory and related areas of mathematics
If you would like to receive information about the upcoming talks, please contact Boris Šobot at
✉ sobot@dmi.uns.ac.rs
Next talk
  • Tuesday, April 5, 2022 - 16:00 CET
    Boris Šobot (Univerzitet u Novom Sadu)

    Kongruencije ultrafiltera

    Apstrakt: Neka je betaN skup ultrafiltera na skupu N prirodnih brojeva, i elementi skupa N su izjednačeni sa glavnim ultrafilterima. Kvaziuređenje | na betaN, ekstenzija relacije deljivosti na N, proučavano je u nekoliko prethodnih radova predavača. Kongruencija po modulu m (m prirodan broj) može se proširiti na prirodan način na betaN. Ispitaćemo, za početak, u kojoj meri se ovo proširenje slaže sa |. Potom ćemo razmotriti dva načina da se definiše i kongruencija po modulu U, gde je U neglavni ultrafilter. Drugi od ta dva načina vodi nas do prirodnog pojačanja relacije deljivosti ultrafiltera |. Razmotrićemo i koliko su ove nove relacije kongruentnosti saglasne sa relacijama deljivosti.

Previous talks:
  • Monday, June 2021
    Stevo Todorčević (University of Toronto and University of Paris)

    Klasifikacije Tukijevskog i Remzijevskog tipa

  • Monday, May 17 and 24, 2021 - 10:15 CET
    Boriša Kuzeljević (University of Novi Sad)

    Tukey order of directed sets

    Abstract: A partially ordered set is said to be directed if every finite subset has an upper bound. In the talk we will introduce the notion of Tukey reducibility between directed sets, and present some basic facts about it. colorings in the free algebra on countably many generators.

  • Monday, May 10, 2021 - 10:15 CET
    Dragan Mašulović (University of Novi Sad)

    Ramsey properties of equationally defined classes of algebras

    Abstract: In this talk we show that nontrivial varieties of algebras enjoy various dual Ramsey properties. The search for dual Ramsey statements has been an important research direction in the past 50 years not only because dual Ramsey results are relatively rare in comparison to the vast number of ``direct'' Ramsey results, but also because they require intricate proof strategies and are usually more powerful than their ``direct'' analogues. It turns out that classes of algebras are a gold mine of dual Ramsey results. In order to prove various dual Ramsey statements for classes of algebras we develop a completely new set of strategies that rely on the fact that right adjoints preserve the Ramsey property while left adjoints preserve the dual Ramsey property. We then consider varieties (that is, equationally defined classes) of algebras as Eilenberg-Moore categories for a monad and show that for every nontrivial variety of algebras all the finite algebras have small dual Ramsey degrees, and that every finite algebra has a finite dual big Ramsey degree with respect to Borel

  • Monday, April 19 and 25, 2021 - 10:15 CET
    Dragan Mašulović (University of Novi Sad)

    Introduction to structural Ramsey theory

    Abstract: Generalizing the classical results of F. P. Ramsey from the late 1920's, the structural Ramsey theory originated at the beginning of 1970's. In this talk we give a brief overview of fundamental results of structural Ramsey theory, explain the problems that the theory has encountered in its 50 year long history, and introduce the modern apparatus of Ramsey degrees (small and big). In the talk we focus on the categorical reinterpretation of basic notions of Ramsey theory.

  • Monday, April 12, 2021 - 10:15 CET
    Anika Njamcul (University of Novi Sad)

    A quest for ideals - generating topology expansions


  • Monday, March 29, 2021 - 10:15 CET
    Aleksandar Pavlović (University of Novi Sad)

    Relations between various types of continuity as consequence of results in Ideal topological spaces


  • Monday, March 22, 2021 - 10:15 CET
    Aleksandar Pavlović (University of Novi Sad)

    Preserving continuity in Ideal topological spaces

    Slides from the talk
  • Monday, March 15, 2021 - 10:15 CET

    Aleksandar Pavlović (University of Novi Sad)

    Ideal topological spaces - Introduction

    Slides from the talk
  • Monday, March 8, 2021 - 10:15 CET

    Boris Šobot (University of Novi Sad)

    Divisibility of ultrafilters - part II

    Slides from the talk
    Abstract: Following a short introduction to nonstandard arithmetic, we will explain its connection to the Stone-Čech compactification, as well as the place of the divisibility relation. Several results will be obtained using nonstandard methods. The main result we will prove is: the divisibility hierarchy contains a copy of the standard order on the reals.
    Apstrakt: Nakon kratkog uvoda u nestandardnu aritmetiku, objasnićemo njenu vezu sa Stone-Čechovom kompaktifikacijom, kao i to kako se deljivost ultrafiltera uklapa u tu vezu. Izvešćemo nekoliko rezultata koristeći nestandardne metode. Glavni rezultat koji dokazujemo je: hijererhija deljivosti ultrafiltera sadrži kopiju standardnog uređenja realnih brojeva.
  • Monday, March 1, 2021 - 10:15 CET

    Boris Šobot (University of Novi Sad)

    Divisibility of ultrafilters - part I

    Slides from the talk
    Abstract: We introduce divisibility relation on the Stone-Cech space of ultrafilters on the set of natural numbers \(\mathbb N\), which is an extension of the ordinary divisibility on \(\mathbb N\). The ordering obtained in this way can be split into two different parts: "the upper one" and "the lower one". In the talk we will discuss the lower part of this hierarchy, where ultrafilters are arranged into levels, similar to the arrangement of natural numbers according to the number of their prime divisors. For example, the first level (without considering number one) consists of prime ultrafilters, the ones divisible only by themselves and unity. However, we will prove that, under CH, for each prime ultrafilter \(U\), at every level there are \(2^{\mathfrak c}\) ultrafilters whose only prime divisor is \(U\).
    Apstrakt: Na Stone-Čechovom prostoru ultrafiltera na skupu prirodnih brojeva \(\mathbb N\) uvodimo relaciju deljivosti, ekstenziju relacije deljivosti na \(\mathbb N\). Uređenje dobijeno na taj način može se podeliti na dva sasvim različita dela: "donji" i "gornji". Na ovom predavanju razmotrićemo donji deo te hijerarhije, na kojem su ultrafilteri podeljeni na nivoe, slično podeli prirodnih brojeva prema broju prostih delilaca. Na primer, prvi nivo (ne računajući jedinicu) čine prosti ultrafilteri: deljivi samo sobom i jedinicom. Dokazaćemo međutim da, uz pretpostavku CH, za svaki prost ultrafilter \(U\) na svakom nivou postoji \(2^{\mathfrak c}\) ultrafiltera čiji je jedini prost delilac \(U\).