Seminar for Mathematical Logic
PROGRAM Program Seminara za logiku za maj 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, 06. maj 2005.G. U 16.15 SATI
NEMA SASTANKA SEMINARA
PETAK, 13. maj 2005.G. U 16.15 SATI
SASTANAK SE NEĆE ODRŽATI ZBOG KONFERENCIJE "RELEVANTNOST LOGIKE"
PETAK, 20. maj 2005.G. U 16.15 SATI
Dragić Banković (Prirodno-matematički fakultet Univerziteta u Kragujevcu)
SISTEMI KONAČNIH JEDNAČINA
(Systems of finite equations)
Na ovom predavanju bice prikazana opsta resenja sistema jednacina na konacnom skupu. Ovaj se rezultat prenosi na visevrednosne logike, Boole-ove algebre i Post-ove algebre. Bice takodje reci o nejednacinama na konacnom skupu, gde se pod nejednacinama podrazumeva formula oblika $f(x) \neq 0$.
PETAK, 27. maj 2005.G. U 16.15 SATI
Justus Diller (Institut fuer Mathematische Logik und Grundlagenforschung der Westfaelischen Wilhelms Universitaet in Muenster)
Concerning my lectures in Belgrade, I consider it best to discuss functional interpretations of Heyting as well as Peano arithmetic in all finite types including a hybrid interpretation of $HA$ which was originally developed by a student of mine, Martin Stein, in the late 1970's and - never having been published - was recently rediscovered by a Danish Student, Joergensen, in the first lecture. I understand that there are experts for Heyting arithmetic, in particular its Kripke models, in Belgrade, e.g. Markovic who in some points cooperated with my former PhD student Kai Wehmeier, now at Irvine, CA, USA. In the second lecture, I want to present functional interpretations of Kripke-Platek and constructive set theory in all finite types, again including a hybrid interpretation which will be passed in for publication hopefully before May. On this basis, I formulate my two abstracts: Part I: Functional interpretations of arithmetic in all finite types
In his 1958 Dialectica interpretation of Heyting arithmetic HA in a quantifier free theory T of primitive recursive functionals of finite type, Goedel reduced the consistency problem of HA to the computability problem of these primitive recursive functionals. We develop functional interpretations that - in contrast to the Dialectica interpretation - extend to Heyting arithmetic in all finite types ($HA^\omega$), the natural union or "span" of HA and Goedel's theory T. We thereby prove closure of $HA^\omega$ under a new form of Markov's rule. Following Shoenfield, we also give an interpretation of Peano arithmetic in all finite types ($PA^\omega$). Finally, we consider hybrids of functional interpretations of $HA^\omega$ which yield closure of this theory under a rule of choice.
Part II: Functional interpretations of set theory We start by developing a theory T^* of constructive set functionals of finite type which employs bounded quantifiers only. In analogy to the interpretations of $PA^\omega$ in the theory T, we give a functional interpretation of Kripke-Platek set theory KP in the theory T^*. We then present the Burr translation for the interpretation of constructive set theory CZF in all finite types in the theory T^* and characterize the strength of this translation. Finally, we study the Schulte hybrid of the Burr interpretation which yields an existence property for CZF which diverges typically from the well known existential definability for HA.
Part I expands on classical material which should be, but is not, part of the background of a well bred logician. Part II covers new material. I am still in contact with Schulte to get his paper on his hybrid into print, and I hope to be through with it before I get to Belgrade. Of course, in Part II also systems in all finite types will be interpreted, but the problems arise already in the standard, type 0 theory. In arithmetic, restriction to type 0 allows G\"odel to get around the use of bounded universal quantifiers. These are characteristic for the Diller-Nahm interpretation of $HA$ in all finite types, just as they are characteristic for a variant of Shoenfield's interpretation of $PA$ in all finite types, and they already used in the corresponding interpretation of $KP$.
OBAVESTENJE 1:
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.
OBAVESTENJE 2:
U Beogradu ovog meseca boravi Gerald J. Massey, Distinguished Professor in Logic, University of Pittsburgh, koji ce odr zati seriju od cetiri predavanja u prostorijama Srpskog filozofskog drustva, Cika Ljubina 18-20, staro Kapetan Misino zdanje (postoji prolaz izmedju prvog i drugog sprata sa sporednog stepenista do Univerzitetske knjizare u novoj zgradi Filozofskog fakulteta do prostorija Drustva).
OBAVESTENJE 3:
Profesor Jean-Francois Pommaret (Ecole Nationale des Pontes et Chaussees, France) odrzace u Matematickom institutu SANU seriju od tri predavanja u ponedeljak, 16 maja 2005. u 12 sati, sredu 18. maja 2005. u 12 sati i cetvrtak, 19. maja 2005 u 11 sati pod opstim naslovom "An introduction to the Galois theory for partial differential equations" Teme su:U Beogradu, 8.05.2005.
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.