東北大学の赤間陽二さんの依頼により投稿します。 小野寛晰 ----------------------------------------------------------------------------------------------
Seminar Announcement
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) akama@m.tohoku.ac.jp, 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%E3%80%80%EF%BC%88english). For the building of the venue, see map on http://www.math.tohoku.ac.jp/map/ http://www.math.tohoku.ac.jp/english/campus-e.html (english)