MISANU

PROGRAM

Plan rada Seminara za logiku za FEBRUAR 2019.

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 22.02.2018. U 14:15, Matematicki institut SANU, sala 301f
Dilip Raghavan, University of Singapore
A SMALL ULTRAFILTER NUMBER
It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets.
It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on ${\aleph}_{\omega+1}$ which is generated by fewer than ${2}^{{\aleph}_{\omega+1}}$ sets.
Zajednicki sastanak odeljenja za Matematiku i Logickog seminara

Petak 22.02.2018. U 16:15, Matematicki institut SANU, sala 301f
Branimir Šešelja, PMF Novi Sad
Ω-ALGEBRAS; ALGEBRAIC AND LOGICAL APPROACH
The research originates in the theory of Ω-sets, introduced in eighties by Fourman and Scott for modeling the intuitionistic logic. Here we extend Ω-sets to Ω-algebras. Namely, given a complete (Heyting) lattice Ω, we get an Ω-algebra (A,E) as a classical algebra A equipped with an Ω-valued compatible equality E with truth-values in Ω. For an Ω-algebra (A,E), inverse images under E of principal filters of elements in Ω, so called cuts of E, are classical congruences on subalgebras of A, i.e., weak congruences on A.
An identity holds on an Ω-algebra if the corresponding lattice-theoretic formula is fulfilled. In addition, an identity holds on (A,E) if and only if the quotient algebras over the mentioned cuts of E fulfil the same identity in the classical way.
We have proved representation theorems for Ω-algebras. Namely, for a particular closure system in the weak congruence lattice of an algebra A, there is a lattice Ω and an Ω-algebra (A,E) such that the cuts of E are the members of the closure system. In addition, every Ω-algebra is accordingly isomorphic to the one constructed in this way. We characterize these closures by particular residuated maps among Ω and the corresponding weak congruence lattice.
As for Ω-sets, the lattice Ω is an algebraization of the logic in which this structure is presented. Following the representation theorems, without loosing relevant algebraic properties (e.g., fulfillment of identities) the lattice Ω can be replaced by the one constructed as a closure system in the weak congruence lattice. In this sense, every Ω-algebra keeps its own local logic.
This is a joint research with Andreja Tepavčević.

OBAVESTENJA:

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