Anyone can come!
Speaker: Norbert Preining (JAIST)
Title: Goedel Logics, Continuous Embeddability and Fraisse's Conjecture
Date: Wednesday, 4 April, 16:00---17:40
Venue: 802, Rigaku Sogo-to (Godo-to), 8F, Science Campus, Tohoku University
Key words: many-valued logic, order theory, semantics
In this talk we present a family of many-valued logics introduced
by Kurt Goedel to approximate Intuitionistic Logic. Later on these
were extended to first order and have exhibited connections to
temporal logics, Kripke frames based logics, fuzzy logics in the
sense of Hajek (t-norm based logics).
These logics are based on selecting a closed subset of the real
interval [0,1], and collecting all formulas evaluating to true
for all valuations into this truth value set. Due to the specific
truth functions different truth values sets might generate the
same logics (as sets of formulas).
During the search for the total number of logics we took up old
conjecture of Fraisse (theorem of Laver) on the behaviour of
scattered linear orderings. We consider continuous embeddability
in the reals and prove a generalized Fraisse conjecture stating
the the closed subsets of the real [0,1] interval with continuous
embeddability are better-quasi-ordered. Using this result we
can show that surprisingly the total number of different Goedel
logics is countable.
This discrepancy - on the one hand uncountable many equivalence
classes of the above mentioned ordering, and countable many
Goedel logics on the other hand - leaves us still without an
"intensional definition" of Goedel logics in the sense that if
two semantical objects (to be found or defined) are different,
then the respective logics are different, too. This does not hold
for equality of the truth value sets, since there are different
truth value sets creating the same logic, as well as for the above
mentioned continuous embeddability induced equivalence.
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Short biography of Norbert Preining
* Graduated from Vienna University of Technology under the
auspicies of the president of the Republic of Austria in 2003
* Postdoc in Siena, Italy as European Community Marie Curie Fellow
* Project leader of a research project of the Austrian Research Fund (FWF)
(paralleling the JSPS)
* Currently Associate Professor at the JAIST
* Secretary of the Kurt Goedel Society, responsible for the Kurt
Goedel Research Prize Fellowship
* Spare time activities are montaineering, typography, TeX, and Debian
Contact: Yohji Akama (Mathematical Institute, Tohoku University)
[email protected], 022-795-7708
For the access, See map on http://www.math.tohoku.ac.jp/access/index.html
or http://www.math.tohoku.ac.jp/english/access-e.html （english).
For the building of the venue, see map on http://www.math.tohoku.ac.jp/map/