### arnold beckmann's pages

## Continuous Fraïssé Conjecture

**File:** PDF-File

**Author:** Arnold Beckmann, Martin Goldstern and Norbert Preining

**Title:** Continuous Fraïssé Conjecture

**Journal:** Order 2008, **25**: 281-298

**DOI:** 10.1007/s11083-008-9094-4

**Abstract:**
We investigate the relation of countable closed
linear orderings with respect to continuous monotone
embeddability and show that there are exactly
ℵ_{1}
many equivalence classes with respect to this embeddability
relation. This is an extension of Laver's result, who considered
(plain) embeddability, which yields coarser equivalence classes.
Using this result we show that there are only
ℵ_{0}
many different Gödel logics.