Skip to main content

Ramsey Theory on Trees and Applications

  • Conference paper
  • First Online:
  • 510 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10119))

Abstract

Modern Ramsey Theory on infinite structures began with the following seminal result of Ramsey.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Avilés, A., Todorcevic, S.: Finite basis for analytic strong \(n\)-gaps. Combinatorica 33(4), 375–393 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Avilés, A., Todorcevic, S.: Types in the \(n\)-adic tree and minimal analytic gaps. Adv. Math. 292, 558–600 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dobrinen, N.: The universal triangle-free graph has finite Ramsey degrees. (2016, in preparation)

    Google Scholar 

  4. Dobrinen, N., Hathaway, D.: The Halpern-Läuchli Theorem at a measurable cardinal (2016, submitted). 15 pages

    Google Scholar 

  5. Dobrinen, N., Laflamme, C., Sauer, N.: Rainbow Ramsey simple structures. Discrete Math. 339(11), 2848–2855 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Džamonja, M., Larson, J., Mitchell, W.J.: A partition theorem for a large dense linear order. Israel J. Math. 171, 237–284 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Džamonja, M., Larson, J., Mitchell, W.J.: Partitions of large Rado graphs. Arch. Math. Logic 48(6), 579–606 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Halpern, J.D., Läuchli, H.: A partition theorem. Trans. Am. Math. Soc. 124, 360–367 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  9. Halpern, J.D., Lévy, A.: The Boolean prime ideal theorem does not imply the axiom of choice. In: Axiomatic Set Theory, pp. 83–134. American Mathematical Society (1971). Proceedings of the Symposium on Pure Mathematics, Vol. XIII, Part I, University California, Los Angeles, Calififornia (1967)

    Google Scholar 

  10. Henson, C.W.: A family of countable homogeneous graphs. Pac. J. Math. 38(1), 69–83 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  11. Komjáth, P., Rödl, V.: Coloring of universal graphs. Graphs Comb. 2(1), 55–60 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  12. Laflamme, C., Sauer, N., Vuksanovic, V.: Canonical partitions of universal structures. Combinatorica 26(2), 183–205 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Milliken, K.R.: A partition theorem for the infinite subtrees of a tree. Trans. Am. Math. Soc. 263(1), 137–148 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ramsey, F.P.: On a problem of formal logic. Proc. Lon. Math. Soc. 30, 264–296 (1929)

    MathSciNet  MATH  Google Scholar 

  15. Sauer, N.: Edge partitions of the countable triangle free homogenous graph. Discrete Math. 185(1–3), 137–181 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sauer, N.: Coloring subgraphs of the Rado graph. Combinatorica 26(2), 231–253 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Shelah, S.: Strong partition relations below the power set: consistency - was Sierpinski right? II. In: Sets, Graphs and Numbers, Budapest, vol. 60, pp. 637–688 (1991). Colloq. Math. Soc. János Bolyai, North-Holland

    Google Scholar 

  18. Todorcevic, S.: Introduction to Ramsey Spaces. Princeton University Press, Princeton (2010)

    MATH  Google Scholar 

  19. Todorcevic, S., Tyros, K.: A disjoint unions theorem for threes. Adv. Math. 285, 1487–1510 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  20. Vlitas, D.: A canonical partition relation for uniform families of finite strong subtrees. Discrete Math. 335, 45–65 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author gratefully acknowledges the support of NSF Grants DMS-142470 and DMS-1600781.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Natasha Dobrinen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag GmbH Germany

About this paper

Cite this paper

Dobrinen, N. (2017). Ramsey Theory on Trees and Applications. In: Ghosh, S., Prasad, S. (eds) Logic and Its Applications. ICLA 2017. Lecture Notes in Computer Science(), vol 10119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54069-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-54069-5_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-54068-8

  • Online ISBN: 978-3-662-54069-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics