Novi Sad group for
Set Theory, Model Theory and General Topology


Department of Mathematics and Informatics
Faculty of Sciences
University of Novi Sad
Trg Dositeja Obradovića 4,
Novi Sad, Serbia
E-mail : settop@dmi.uns.ac.rs

Supported by:

Ministry of Education,
Science and Technological Development
of the Republic of Serbia
Project number 174006

Science Fund of the Republic of Serbia


SEMINAR "FUNDAMENTI MATEMATIKE"

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.



NOVI SAD CONFERENCES in Set Theory and General Topology







PAST AND CURRENT RESEARCH TOPICS
POSETS OF SUBMODELS:

We investigate the collections of (elementary) submodels of first order structures ordered by the inclusion and some other natural orderings. These partial orders are observed from the aspect of set theory, their cardinal and order invariants are explored and they are examined as forcing notions as well.

SET-THEORETIC FORCING:

The conditions under which forcing violates certain structures of a given model of set theory, such as ultrafilters, maximal almost disjoint families and inseparable sequences, are investigated.

BI-CONDENSABILITY AND REVERSIBILITY:

We study the condensational preorder on the class of all relational structures, induced by bijective homomorphisms (condensations), and the corresponding equivalence relation of bi-condensability. Emphasis is put on investigating the class of structures that have the property Cantor-Schroeder-Bernstein with respect to that preorder, including the structures for which each bijective endomorphism is an automorphism (the so called reversible structures).

GAMES ON BOOLEAN ALGEBRAS:

The cut-and-choose games on Boolean algebras are examined, searching for equivalent conditions for the existence of winning strategies and for the examples of Boolean algebras on which the games have different outcomes.

CONVERGENCE STRUCTURES ON BOOLEAN ALGEBRAS:

The topologies on complete Boolean algebras generated by convergence structures are explored. The relations between the topological properties of the spaces obtained in this way and the algebraic and forcing properties of the corresponding Boolean algebras are examined.

TOPOLOGICAL SPACES OBTAINED BY IDEALS:

From a starting topology there are several ways to generate a new topology by an ideal on the ground set. We study differences and similarities between those new topologies, depending on properties of the starting topology and the ideal.