2005 seminar talk: Continuous Fraisse conjecture and the number of Gödel logics

Talk held by Martin Goldstern (TU Wien) at the KGRC seminar on 2005-01-18.


Linear orders are naturally quasiordered by embeddability. Answering a question of Fraisse, Laver showed that this quasiorder, restricted to the scattered linear orders (those that do not contain a copy of the rationals), is a well-quasi-order; he also showed that there are exactly aleph1 equivalence classes (modulo bi-embeddability) of countable linear orders. In a joint paper with Arnold Beckmann and Norbert Preining we generalize this theorem to the natural quasiorder that is given by CONTINUOUS embeddability. A Gödel logic is given by a closed subset G of the unit intervall (containing 0 and 1). Fuzzy (relational) G-models are sets M with maps M^k -> G for every k-ary predicate symbol. A fuzzy satisfaction function is defined naturally; the "Gödel logic" associated with G is the set of all sentences which have value 1 in every fuzzy G-model. All these logics are contained in the set of classical validities; as an application of the continuous Fraisse conjecture, we show that there are only countably many Gödel logics.

Bottom menu

Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2010-12-16, 04:37.