Project name: Set-theoretic, model-theoretic and
Ramsey-theoretic phenomena in mathematical structures:
similarity and diversity, SMART (2022-2025)
Project Reference No: 7750027, supported by the Science Fund of the Republic of Serbia
Project leader: Miloš Kurilić
Project description
We investigate set-theoretic, model-theoretic, combinatorial and
topological properties of mathematical structures and their interplay,
as well as several preorders and similarity relations on classes of
structures.
The main objectives are:
- To develop classification techniques for studying isomorphism types
of countable models and confirm Vaught's conjecture for new classes
of theories (weakly o-minimal, NIP theories with built-in Skolem functions
and theories of partial orders of larger Dushnik-Miller dimension);
- To obtain general results concerning the classification of relational
structures (in particular, of Fraïssé limits) and their self-embedding
monoids, related to the forcing equivalence and the cardinal and order
invariants of their posets of copies; to explore the role of the Sacks
forcing in this context;
- To investigate the phenomena related to the preorder induced by
bijective homomorphisms between structures (condensational equivalence,
reversibility) modifying model-theoretic methods (Ehrenfeucht-Fraïssé
games, forcing isomorphism, Scott sentences) and to apply these techniques
in investigation of particular classes of structures (as posets, graphs);
- To explore the behavior of dual big Ramsey degrees in countable
structures and to investigate the behavior of the dual Ramsey property
in the infinite (three stages: canonical dual Ramsey property for finite
chains and permutations, for finite edge-ordered graphs, infinite dual
Ramsey property for structures);
- To explore the construction of iterated nonstandard models with high
degree of saturation and their possible applications;
- To investigate the forcing related properties of several topologies
on Boolean algebras as well as the properties of the topologies generated
by the local closure function in ideal topological spaces (e.g.
covering properties, behavior under mappings).
List of researchers
| Miloš Kurilić |
|
Full professor |
|
Faculty of Sciences, University of Novi Sad |
|
milos@dmi.uns.ac.rs |
| Stevo Todorčević |
|
Research professor |
|
Mathematical Institute SANU |
|
stevo@mi.sanu.ac.rs |
| Predrag Tanović |
|
Research professor |
|
Mathematical Institute SANU |
|
tane@mi.sanu.ac.rs |
| Dragan Mašulović |
|
Full professor |
|
Faculty of Sciences, University of Novi Sad |
|
masul@dmi.uns.ac.rs |
| Aleksandar Pavlović |
|
Associate professor |
|
Faculty of Sciences, University of Novi Sad |
|
apavlovic@dmi.uns.ac.rs |
| Boris Šobot |
|
Associate professor |
|
Faculty of Sciences, University of Novi Sad |
|
sobot@dmi.uns.ac.rs |
| Slavko Moconja |
|
Assistant professor |
|
Faculty of Mathematics, University of Belgrade |
|
slavko@matf.bg.ac.rs |
| Boriša Kuzeljević |
|
Assistant professor |
|
Faculty of Sciences, University of Novi Sad |
|
borisha@dmi.uns.ac.rs |
| Aleksandar Janjoš |
|
Teaching assistant |
|
Faculty of Sciences, University of Novi Sad |
|
aleksandar.janjos@uns.ac.rs |
