Order

, Volume 22, Issue 3, pp 289–300 | Cite as

Universality of Embeddability Relations for Coloured Total Orders

Article

Abstract

Some examples of Σ11-universal preorders are presented, in the form of various relations of embeddability between countable coloured total orders. As an application, strengthening a theorem of (Marcone, A. and Rosendal, C.: The Complexity of Continuous Embeddability between Dendrites, J. Symb. Log.69 (2004), 663–673), the Σ11-universality of continuous embeddability for dendrites whose branch points have order 3 is obtained.

Mathematics Subject Classification (2000)

03E15 06A05 

Key Words

coloured total order Borel reducibility Σ11-universality dendrite 

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References

  1. 1.
    Friedman, H. and Stanley, L.: A Borel reducibility theory for classes of countable structures, J. Symb. Log. 54 (1989), 894–914.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hjorth, G.: Classification and Orbit Equivalence Relations, American Mathematical Society 2000.Google Scholar
  3. 3.
    Kechris, A. S.: Classical Descriptive Set Theory, Springer, 1995.Google Scholar
  4. 4.
    Laver, R.: On Fraïssé’s order type conjecture, Ann. Math. 93 (1971), 89–111.CrossRefMathSciNetGoogle Scholar
  5. 5.
    Louveau, A. and Rosendal, C.: Relations d’équivalence analytiques complètes, Comptes Rendus de l’Académie des Sciences. Série I 333 (2001), 903–906.MATHMathSciNetGoogle Scholar
  6. 6.
    Marcone, A.: Foundations of bqo theory, Trans. Am. Math. Soc. 345 (1994), 641–660.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Marcone, A. and Rosendal, C.: The Complexity of Continuous Embeddability between Dendrites, J. Symb. Log. 69 (2004), 663–673.CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Nadler Jr., S. B.: Continuum Theory, Dekker, 1992.Google Scholar
  9. 9.
    Rosenstein, J. G.: Linear Orderings, Academic Press, 1982.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Dipartimento di matematicaPolitecnico di TorinoTorinoItaly

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