ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

**Seminar for Mathematical Logic**

**PROGRAM**

** Plan rada Seminara za logiku za novembar 2014. **

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, 7.11.2014. U 16:15 (MI SANU, 301f) **

* Vladimir Odrljin, Zagreb *

** CONCEPTS, IDENTIFICATION OF OBJECTS AND SOLUTION OF RUSSELL'S PARADOX**

Abstract: In this presentation, sets whose elements denote objects are especially observed. Denotation is made in accordance with Frege's semantics. These sets, whose elements denote some objects, are associated with complex issues. The solutions to these problems are performed using the aforementioned identification of objects. Here we use the entity-relationship model, which is based on the assumption that the world is discrete, that is, that the world consists of objects and their relationships. The entities are constructed using properties. One of the mathematicians who defined this model was K. Godel. He published it in 1944. Leibniz's law enables work on the identification of entities. By using this law we assure that the identification of the object is a mathematical discipline. Since the world is represented by the entity-relationship model, then it follows that sets with elements that denote objects in the real world are numerous and important. Regarding mathematical sets, which have arbitrary members, we use Frege's results. Frege defined two ways of determining sets, by extension and intension. Both of these ways must give the same elements of a set. When we use the concept for determining a set, we use two semantic procedures, which are based on concepts and identification of objects. In this presentation, the following two things are especially highlighted.

(i) Concepts do not construct elements of a set. Concepts just ``check'' which of the existing and identified objects belong to one set.

(ii) When we construct a set, then we need to identify (determine) its members.

**Petak, 14.11.2014. U 16:15 (MI SANU, 301f)**

* Borisa Kuzeljevic, Matematicki institut SANU, Beograd *

**FORCING BY MATRICES OF COUNTABLE, ELEMENTARY SUBMODELS **

Abstract: In his paper from 1984. ``A note on the proper forcing axiom'' Todorcevic introduced a method of forcing by a chain of countable elementary submodels, which turned out to be one of the most successful approaches to constructing proper partial orders. In a note at the end of the paper a generalization of the method was suggested, that became actual in the past few years. The talk will contain an exposition of Todorcevic's method and the suggested generalization will be discussed.

**PETAK, 21.11.2014. U 16:15 (MI SANU, 301f) **

* Nedeljko Stefanovic, Beograd *

** ELEMENTARNA TEORIJA IZRACUNLJIVOSTI I**

Apstrakt: Predavanje obuhvata elementarne pojmove teorije izracunljivosti, ukljucujuci i Tjuringove stepene.

**PETAK, 28.11.2014. U 16:15 (MI SANU, 301f) **

* Nedeljko Stefanovic, Beograd *

** ELEMENTARNA TEORIJA IZRACUNLJIVOSTI II **

Apstrakt: Ovo je nastavak predavanja odranog prethodne nedelje. Predavanje obuhvata elementarne pojmove teorije izraljivosti, uklju i Tjuringove stepene.

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