Linear orders are naturally quasiordered by embeddability. Answering a question of Fraïssé, 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 \(\aleph_1\) 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 interval (containing 0 and 1). Fuzzy (relational) \(G\)-models are sets \(M\) with maps \(M^k\to G\) 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.