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