MISANU

PROGRAM

Predavanja na Logičkom seminaru možete uživo pratiti preko linka
https://miteam.mi.sanu.ac.rs/asset/iYxPidYtFqBC9sT7a.
Ukoliko želite i da učestvujete u diskusiji, to možete preko linka
https://miteam.mi.sanu.ac.rs/asset/oaqCm4EyPhHR6kM6N
na kome prethodno treba napraviti nalog, t.j. popuniti registracioni formular koji se pojavi nakon klika.

SREDA, 07.06.2023. u 13:00, Kneza Mihaila 36, sala 301f i On-line
Alexey Semenov, Department of Mathematical Logic and Theory of Algorithms of Lomonosov Moscow State University; Axel Berg Institute of Cybernetics and Educational Computing of Russian Academy of Sciences; Russian Academy of Sciences; Russian Academy of Education
THE THEORY OF DEFINABILITY
Definability theory can be considered as an important part of all mathematics along with proof theory, model theory, and computation theory. This was constantly emphasized by Alfred Tarski, who owns remarkable results in this theory, the main question of which is: is it possible to define some concept or relation, through other concepts, relations.
The report will give a general overview of the results in definability theory since the XIX century, including the Svenonius Theorem (completeness theorem for definability), the latest results of the author, his students and colleagues are presented, and a wide spectrum of open problems and possible solutions are proposed. The presence of this spectrum is a characteristic feature of the current state of definability theory.
The report can also provide a general overview of the research on mathematical logic, theory of algorithms and Computer Science going on at Moscow University, Moscow, and Russia.
Zajednicki sastanak Logickog seminara i Odeljenja za matematiku.

PETAK, 09.06.2023. u 16:15, Kneza Mihaila 36, sala 301f i On-line
Marko Stanković, University of Niš, Pedagogical Faculty in Vranje
COMPUTATION OF BISIMULATION FOR FUZZY MULTIMODAL LOGICS AND HENESSY-MILNER TYPE THEOREMS
Here we study fuzzy multimodal logics over a complete Heyting algebra and Kripke models for these logics. We introduce two types of simulations (forward and backward) and five types of bisimulations (forward, backward, forward-backward, backward-forward and regular) between Kripke models. For each type of simulations and bisimulations an efficient computation algorithm has been provided. We also demonstrate the application of these algorithms in the state reduction of Kripke models. We show that forward bisimulation fuzzy equivalences on the Kripke model provide reduced models equivalent to the original model concerning plus-formulae, backward bisimulation fuzzy equivalences provide reduced models equivalent concerning minus-formulae, while regular bisimulation fuzzy equivalences provide reduced models equivalent concerning all modal formulae.
Furthermore, for a given non-empty set Ψ of modal formulae, we introduce the concept of a weak bisimulation between Kripke models. This concept can be used to express the degree of modal equivalence between worlds w and w′ with respect to the formulae from Ψ. In this regard, we prove several Hennessy-Milner type theorems.

SREDA, 21.06.2023. u 14:15, Kneza Mihaila 36, sala 301f i On-line
Predrag Tanović, Mathematical Institute SANU
ON VAUGHTS CONJECTURE FOR COLORED TREES
By a tree we mean a partial order in which every pair of elements has inf and predecessors of any element are linearly ordered. A colored tree has arbitrary unary predicates added. Steel in 1978 proved a strong form of Vaught's conjecture for colored trees: any $L_{\omega_1,\omega}$-sentence in a language of colored trees has either perfectly many or at most $\aleph_0$ countable models.
The talk will contain a sketch of a purely first-order proof of the original version of the conjecture: a complete first-order theory $T$ of colored trees has either continuum or at most $\aleph_0$ countable models. The proof relies on `geometric' properties of definable sets and types in colored trees. They enable, if $T$ has few countable models and $M\models T$, coding the isomorphism type of $M$ by a certain labeled subtree of (uniformly) finite height. The labels are isomorphism types of substructures induced on certain linear sub-orders of the tree so, inevitably, we will rely on our joint work with Moconja and Ilic on `elimination of quantifiers' (description of definable sets) for colored linear ordea proof of rs and on a proof of Vaught's conjecture for theories colored linear orders.
This research was supported by the Science Fund of the Republic of Serbia, Grant No. 7750027: Set-theoretic, model-theoretic and Ramsey-theoretic phenomena in mathematical structures: similarity and diversity – SMART,

OBAVEŠTENJA:

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

Beograd,
Srdacan pozdrav,

rukovodilac seminara Predrag Tanovic