We investigate the relation of countable closed subsets of the reals withrespect to continuous monotone embeddability; we show that there are exactlyaleph_1 many equivalence classes with respect to this embeddability relation. This is an extension of Laver's 1971 result, who considered (plain)embeddability, which yields coarser equivalence classes. Using this result we show that there are only countably many different Godellogics.
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