Skip to main content
SpringerLink
Log in

The ℵ 0-categorical Trees

  • Published:
Order Aims and scope Submit manuscript

Abstract

We provide a description of the structure of ℵ 0-categorical trees. First the maximal branches of ℵ 0-categorical tree are examined, followed by the configuration of the ramification orders, which are then combined to provided necessary and sufficient conditions for a tree to be ℵ 0-categorical in terms of these two things.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barham, R.: The reconstruction of cycle-free partial orders from their abstract automorphism groups I : Treelike CFPOs. arXiv:1502.02520

  2. Chicot, K.M.: Transitve properties of countable trees. PhD thesis, University of Leeds (2004)

  3. Droste, M.: Structure of partially ordered sets with transitive automorphism groups. Memoirs of the A.M.S., v.57 (1985)

  4. Droste, M., Holland, W.C., Macpherson, H.D.: Automorphism groups of infinite semilinear orders (i). Proceedings of the L.M.S. 58, 454–478 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  5. Droste, M., Holland, W.C., Macpherson, H.D.: Automorphism groups of infinite semilinear orders (ii). Proceedings of the L.M.S. 58, 479–494 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  6. Droste, M., Holland, W.C., Macpherson, H.D.: Automorphism groups of infinite semilinear orders: Normal subgroups and commutators. Can. J. Math. 43(4), 721–737 (1991)

    Article  MATH  Google Scholar 

  7. Hodges, W.: Model theory. Cambridge University Press (1993)

  8. Mwesigye, F., Truss, J.K.: Countable categorical coloured linear orders. Math. Log. Q 56(2), 159–163 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  9. Rosenstein, J.G.: ℵ 0-categoricity of linear orderings. Fund. Math. 64, 1–5 (1969)

    MathSciNet  MATH  Google Scholar 

  10. Rosenstein, J.G.: Linear orderings. Academic Press (1982)

  11. Rubin, M.: The Reconstruction of Trees from their Automorphism Groups. Contemporary mathematics (American Mathematical Society) (1991)

  12. Simon, P.: On dp-minimal ordered structures. J. Symbolic Logic 76(2), 448–460 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Warren, R.: The structure of k-cs-transitive cycle-free partial orders. Memoirs of the A.M.S., v.129 (1997)

Download references

Author information

Authors and Affiliations

  1. Institut für Algebra, Technische Universität, Dresden, Germany

    Robert Barham

Authors
  1. Robert Barham
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Barham.

Additional information

The author has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 257039).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Barham, R. The ℵ 0-categorical Trees. Order 34, 127–138 (2017). https://doi.org/10.1007/s11083-016-9391-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11083-016-9391-2

Keywords

Search

Navigation