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, 25:281 | Cite as

Continuous Fraïssé Conjecture

  • Arnold Beckmann
  • Martin GoldsternEmail author
  • Norbert Preining
Article

Abstract

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.

Keywords

Better quasi order Gödel logic Wellquasiorder Fraisse conjecture Continuous embeddings 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Arnold Beckmann
    • 1
  • Martin Goldstern
    • 2
    Email author
  • Norbert Preining
    • 2
  1. 1.Department of Computer ScienceSwansea UniversitySwanseaUK
  2. 2.Institute of Discrete Mathematics and GeometryVienna University of TechnologyWienAustria

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