Seminar for
Mathematical Logic
PROGRAM
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
PETAK, 13. maj 2005.G. U 16.15 SATI
PETAK, 20. maj 2005.G. U 16.15 SATI
PETAK, 27. maj 2005.G. U 16.15 SATI
OBAVESTENJE 1:
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 .
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.
OBAVESTENJE 2:
OBAVESTENJE 3:
U Beogradu, 8.05.2005.
Rukovodioci seminara:
Azurirani programi svih seminara Matematickog instituta SANU mogu se naci
na adresi www.mi.sanu.ac.yu.
Program Seminara za logiku za maj 2005
NEMA SASTANKA SEMINARA
SASTANAK SE NEĆE ODRŽATI ZBOG KONFERENCIJE "RELEVANTNOST LOGIKE"
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 $f(x) \neq 0$.
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 $KP$.
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.
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.
Petak, 6. maj 2005.g. u 12 sati, "Quine's Indeterminacy-of-Translation
Thesis:
What does it mean? Is it really true?"
Petak, 13. maj 2005.g. u 12 sati, "St. Thomas Aquinas' on the age of the
universe: Impressive Creativity or Intellectual Dishonesty?"
Petak, 27. maj 2005.g. u 12 sati, "Modal epistemology: On inferences from
conceivability to possibility"
Petak, 3. juni 2005.g. u 12 sati, "Semantic holism: Does inference determine
semantics?" (Suorganizator ovog poslednjeg predavanja je takodje Seminar za
logiku)
1)From pure algebra to partial differential algebra,
2) From Lie groups to Lie pseudogroups
3) From classical Galois theory to differential Galois theory.
Dr. Djordje Vukomanovic i Dr. Kosta Dosen.