Seminar for Mathematical Logic

PROGRAM

Plan rada Seminara za logiku za oktobar 2015.

Seminar za matematicku logiku Matematickog instituta SANU nastavlja rad u letnjem semestru 2011/2012.g. na ovoj adresi: Kneza Mihaila 36/III sprat, soba 301f - sala za seminare. Cetvrtkom posle podne, ali od 15:00 sati, odrzavace se predavanja na Seminaru iz verovatnosnih logika pod rukovodstvom Profesora Miodraga Raskovica koji je u decembru 2007. dobio akreditaciju Naucnog veca Instituta. Na taj nacin, ponovo, kao pre vise decenija, postoje dva logicka seminara.

PETAK, 2.10.2015. U 16:15 (MI SANU, 301f)
Predrag Tanovic, Beograd
LINEARNA UREDJENJA, I DEO

Rezime: U prvom iz serije predavanja o modelsko teorijskim osobinama linearnih uredjenja bice dat istorijski osvrt na tu oblast i najavljen sadrzaj ostalih predavanja. Cilj serije je predstavljanje par Rezime: U prvom iz serije predavanja o modelsko teorijskim osobinama linearnih uredjenja bice dat istorijski osvrt na tu oblast i najavljen sadrzaj ostalih predavanja. Cilj serije je predstavljanje par elementarnih rezultata iz disertacija Slavka Moconje i Dejana Ilica.

PETAK, 9.10.2015. U 16:15 (MI SANU, 301f)
Krzysztof Krupinski, University of Wroclav, Poland
THE COMPLEXITY OF STRONG TYPES

Abstract: Let $\C$ be a monster model of an arbitrary first order theory. We study bounded, invariant equivalence relations on $\C$ (or even on products of sorts of $\C$). If such a relation refines the relation of having the same type over $\emptyset$, then its classes are called strong types (sometimes the relation itself is called a strong type). Certain particular strong types play a fundamental role in model theory (mainly Shelah, Kim-Pillay and Lascar strong types). In the case where a bounded, invariant equivalence relation $E$ is type-definable, the quotient $\C/E$ equipped with the so-called logic topology is a compact, Hausdorff space, so the logic topology is a good tool to study this quotient. If, however, $E$ is only (bounded) invariant, then the logic topology on $\C/E$ is not necessarily Hausdorff (and may even by trivial), so a question arises how to view $\C/E$ as a mathematical object and how to measure its complexity. The first step is to look at the cardinality of this quotient, but more meaningful is to look at the Borel cardinality in the sense of descriptive set theory (which requires the assumption that the language is countable). I will discuss both things, concluding with very general, comprehensive results from my recent paper (joint with A. Pillay and T. Rzepecki) which relate type-definability, relative definability, smoothness (in the sense of descriptive set theory) and the number of classes of bounded, invariant equivalence relations. The main tool used in the proofs of these results is topological dynamics for the group of automorphisms of $\C$ which we developed in the same paper, but it will not be enough time during my talk to touch this topic as well.

PETAK, 16.10.2015. U 16:15 (MI SANU, 301f)
Slavko Moconja
LINEARNA UREDJENJA, II DEO

PETAK, 30.10.2015. U 16:15 (MI SANU, 301f)
Dejan Ilic, Slavko Moconja, Predrag Tanovic
LINEARNA UREDJENJA, III DEO

OBAVESTENJA:

Ukoliko zelite mesecne programe ovog Seminara u elektronskom obliku, obratite se: zpetric@mi.sanu.ac.rs ili tane@mi.sanu.ac.rs. Programi svih seminara Matematickog instituta SANU nalaze se na sajtu: www.mi.sanu.ac.rs



Beograd,
Srdacan pozdrav,

rukovodioci seminara Zoran Petric i Predrag Tanovic