Continuous Fraïssé Conjecture

We will investigate the relation of countable closed linear orderings with respect to continuous monotone embeddability and will show that there are exactly $\aleph_1$ many equivalence classes with respect to this embeddability relation. This is an extension of Laver’s result (Laver, Ann. Math. 93(2):89–111, 1971), who considered (plain) embeddability, which yields coarser equivalence classes. Using this result we show that there are only $\aleph_0$ many different Gödel logics.

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