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

Seminar for Mathematical Logic

 

PROGRAM Program Seminara za logiku za april 2005

Sastanci Seminara za matematicku logiku Matematickog instituta SANU odrzavace se i u akademskoj 2004/2005. godini po pravilu petkom od 16:15 sati u sali 2 na I spratu zgrade SANU, Beograd, Kneza Mihaila 35.

PETAK, 01. april 2005.G. U 16.15 SATI
Djordje Vukomanović (Gradjevinski fakultet, Univerziteta u Beogradu)
IMPLIKACIJA I MREŽE
(Implication and lattices)


The chief purpose of this lecture is to show that the theory of positive implication algebras provides a complete characterization of intuitionistic implication, as defined on Heyting algebras. This is accomplished by showing that every positive implication algebra can be embedded into a dual symmetrical Heyting algebra (of implicative filters of the given algebra) dually preserving intuitionistic implication, thus yielding completeness. Moreover, such a symmetrical Heyting algebra is obviously dually isomorphic to itself. The same applies, mutatis mutandis, to the theory of S4 implication algebras which provides a complete characterization of S4 implication as defined on finitely deductive lattices. That is, every S4 implication algebra can be embedded into a dual finitely deductive lattice dually preserving S4 implication.

PETAK, 08. april 2005.G. U 16.15 SATI
Nada Perić (postdiplomac Departmana za matematiku i informatiku Prirodnomatematičkog fakulteta Univerziteta u Novom Sadu)
NEKI IDEALI NA SKUPU PRIRODNIH BROJEVA I ODGOVARAJUĆE INVARIJANTE KONTINUUMA
(Some ideals on the set of natural numbers and the corresponding invariants of the continuum)


U ovoj magistarskoj tezi (Poglavlja: 1. Mali kardinali (Small cardinals), 2. Mali kardinali odredjeni proizvoljnim idealom (Small cardinals assigned with arbitrary ideal), 3. Neki specijalni ideali i kardinalnost odgovarajucih skoro disjunktnih familija (Some special ideals and and the cardinality of the corresponding almost disjoint families)) dat je pregled vec poznatih rezultata iz oblasti malih kardinala (invarijanata kontinuuma): b, d, p, t, a, s, u. Pored toga, umesto ideala konacnih skupova posmatramo i proizvoljan ideal i ispitujemo osobine odgovarajucih invarijanata kontinuuma i njihove odnose. U originalnom delu teze analizirana su tri konkretno izabrana ideala: ideal generisan ograni.cenim rastucim nizovima racionalnih brojeva, ideal generisan ogranicenim rastucim i ogranicenim opadajucim nizovima racionalnih brojevima i ideal nigde gustih skupova i ispitivane su osobine odgovarajucih malih kardinala.
(In this thesis we give a survey of known results concerning small cardinals (invariants of the continuum): b, d, p, t, a, s, u. Besides, instead of the ideal of finite sets we consider an arbitrary ideal and investigate the corresponding invariants of the continuum and their relationship. In the original part of the thesis three special ideals are analyzed: the ideal generated by bounded, increasing sequences of rational numbers, the ideal generated by bounded increasing and bounded decreasing sequences of rational numbers, and the ideal of nowhere dense sets. The properties of the corresponding small cardinals are investigated.)

PETAK, 15. april 2005.G. U 16.15 SATI
Zoran Petrić (Matematički institut SANU, Beograd)
KOHERENCIJA I KONFLUENCIJA
(Coherence and confluence)


U ovom predavanju bice reci o vezi izmedju kategorijalnog pojma koherencije i pojma konfluencije u sistemima redukcija.
(This talk is about a connection between the categorial notion of coherence and teh rewriting notion of confluence).

PETAK, 22. april 2005.G. U 16.15 SATI
Melanija Mitrović (Mašinski fakultet Univerziteta u Nisu)
PREDSTAVLJANJE KNJIGE "POLUMREŽE ARHIMEDOVIH POLUGRUPA"
(Presentation of the book Semilattices of Archimedean semigroups, University of Nis, Faculty of Mechanical Engineering, 2004, pp. 160)


From the Foreword by Donald B. McAlister: Semigroups are, by definition, simple objects but the very simplicity of their definition means that they can have a very complicated and intricate structure. Various approaches have been developed over the years to construct frameworks for understanding this structure. The present work provides a detailed study of one of these approaches, namely through semilattice decompositions. This approach was pioneered by A.H.Clifford in 1940s and extended by T. Tamura, for commutative semigroups, and others including M. Petrich and, in particular, the members of the Nis school of semigroup theory, led by S. Bogdanovic, to more general situations. The present book provides a competent and valuable exposition of the approach to the structure theory of semigroups through semilattice decompositions. It should be a useful resource for those working on the decomposition theory of semigroups and for those in other areas who wish to have access to a concise account of this area.

Petak 29. april 2005.G. U 16.15 SATI
Sastanak Seminara nece biti odrzan zbog Uskrsnjih i Prvomajskih praznika

OBAVESTENJE 1:

Sastanak Konferencijskog komiteta Konferencije Relevantnost logike odrzace se u petak, 15. aprila 2005. s pocetkom u 15:00 sati u Biblioteci Matematickog instituta SANU

OBAVESTENJE 2:

RELEVANTNOST LOGIKE - KONFERENCIJA U SPOMEN ALEKSANDRU KRONU (1937-2000), BEOGRAD, 12 - 14 MAJ 2005

Seminar za Matematicku logiku Matematickog instituta SANU, Filozofski fakultet Univerziteta u Beogradu i Drustvo za cistu i primenjenu logiku organizuju komemorativnu konferenciju povdom petogodisnjice smrti Aleksandra Krona, Profesora Filozofskog fakulteta i jednog od osnivaca i dugogodisnjeg rukovodioca ovog Seminara. Prijave na Konferenciju i rezimee (do 5 redova) treba slati do 15. aprila 2005.g. na adresu: rellog@mi.sanu.ac.yu .
Konferencijski komitet: Slavisa Presic, Zoran Markovic, Zarko Mijajlovic, Miodrag Kapetanovic, Milan Bozic, Slobodan Vujosevic, Djordje Vukomanovic, Kosta Dosen, Zivan Lazovic, Svetlana Knjazeva-Adamovic, Aleksandar Perovic, Milos Milosevic.

THE RELEVANCE OF LOGIC - CONFERENCE IN MEMORY OF ALEKSANDAR KRON (1937 - 2000), BELGRADE, 12 - 14 MAY 2005

The Logic Seminar of the Mathematical Institute of the Serbian Academy of Sciences and Arts, the Faculty of Philosophy of the University of Belgrade and the Society for Pure and Applied Logic will organize a conference with the title above to commemorate the fifth anniversary of the death of Aleksandar Kron. Submissions for the conference and abstracts (up to 5 lines) should be sent to: rellog@mi.sanu.ac.yu , before 15 April 2005.
Conference Committee: Slavisa Presic, Zoran Markovic, Zarko Mijajlovic, Miodrag Kapetanovic, Milan Bozic, Slobodan Vujosevic, Djordje Vukomanovic, Kosta Dosen, Zivan Lazovic, Svetlana Knjazeva-Adamovic, Aleksandar Perovic, Milos Milosevic.

U Beogradu, 1.04.2005.

Rukovodioci seminara:
Dr. Djordje Vukomanovic i Dr. Kosta Dosen.

Azurirani programi svih seminara Matematickog instituta SANU mogu se naci na adresi www.mi.sanu.ac.yu.