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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Avilés, A., Todorcevic, S.: Finite basis for analytic strong \(n\)-gaps. Combinatorica 33(4), 375–393 (2013)
Avilés, A., Todorcevic, S.: Types in the \(n\)-adic tree and minimal analytic gaps. Adv. Math. 292, 558–600 (2016)
Dobrinen, N.: The universal triangle-free graph has finite Ramsey degrees. (2016, in preparation)
Dobrinen, N., Hathaway, D.: The Halpern-Läuchli Theorem at a measurable cardinal (2016, submitted). 15 pages
Dobrinen, N., Laflamme, C., Sauer, N.: Rainbow Ramsey simple structures. Discrete Math. 339(11), 2848–2855 (2016)
Džamonja, M., Larson, J., Mitchell, W.J.: A partition theorem for a large dense linear order. Israel J. Math. 171, 237–284 (2009)
Džamonja, M., Larson, J., Mitchell, W.J.: Partitions of large Rado graphs. Arch. Math. Logic 48(6), 579–606 (2009)
Halpern, J.D., Läuchli, H.: A partition theorem. Trans. Am. Math. Soc. 124, 360–367 (1966)
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)
Henson, C.W.: A family of countable homogeneous graphs. Pac. J. Math. 38(1), 69–83 (1971)
Komjáth, P., Rödl, V.: Coloring of universal graphs. Graphs Comb. 2(1), 55–60 (1986)
Laflamme, C., Sauer, N., Vuksanovic, V.: Canonical partitions of universal structures. Combinatorica 26(2), 183–205 (2006)
Milliken, K.R.: A partition theorem for the infinite subtrees of a tree. Trans. Am. Math. Soc. 263(1), 137–148 (1981)
Ramsey, F.P.: On a problem of formal logic. Proc. Lon. Math. Soc. 30, 264–296 (1929)
Sauer, N.: Edge partitions of the countable triangle free homogenous graph. Discrete Math. 185(1–3), 137–181 (1998)
Sauer, N.: Coloring subgraphs of the Rado graph. Combinatorica 26(2), 231–253 (2006)
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
Todorcevic, S.: Introduction to Ramsey Spaces. Princeton University Press, Princeton (2010)
Todorcevic, S., Tyros, K.: A disjoint unions theorem for threes. Adv. Math. 285, 1487–1510 (2015)
Vlitas, D.: A canonical partition relation for uniform families of finite strong subtrees. Discrete Math. 335, 45–65 (2014)
Acknowledgments
The author gratefully acknowledges the support of NSF Grants DMS-142470 and DMS-1600781.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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)