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1 - Ramsey classes: examples and constructions

Published online by Cambridge University Press:  05 July 2015

Artur Czumaj
Affiliation:
University of Warwick
Agelos Georgakopoulos
Affiliation:
University of Warwick
Daniel Král
Affiliation:
University of Warwick
Vadim Lozin
Affiliation:
University of Warwick
Oleg Pikhurko
Affiliation:
University of Warwick
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Print publication year: 2015

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References

[1] F. G., Abramson and L., Harrington, Models without indiscernibles, Journal of Symbolic Logic 43 (1978), no. 3, 572–600.Google Scholar
[2] S. A., Adeleke and P. M., Neumann, Relations related to betweenness: their structure and automorphisms, Memoirs of the AMS, vol. 623, American Mathematical Society, 1998.
[3] J. H., Bennett, The reducts of some infinite homogeneous graphs and tournaments, Ph. D. Thesis, 1997.
[4] M., Bodirsky, Cores of countably categorical structures, Logical Methods in Computer Science 3 (2007), no. 1, 1–16.Google Scholar
[5] M., Bodirsky, Complexity classification in infinite-domain constraint satisfaction, 2012.
[6] M., Bodirsky, New Ramsey classes from old, Electronic Journal of Combinatorics 21 (2014), no. 2. Preprint arXiv:1204.3258.Google Scholar
[7] M., Bodirsky, M., Hils, and B., Martin, On the scope of the universalalgebraic approach to constraint satisfaction, Logical Methods in Computer Science (LMCS) 8 (2012), no. 3:13. An extended abstract that announced some of the results appeared in the proceedings of Logic in Computer Science (LICS–10).Google Scholar
[8] M., Bodirsky and D., Piguet, Finite trees are Ramsey with respect to topological embeddings, 2010.
[9] M., Bodirsky and M., Pinsker, Reducts of Ramsey structures, AMS Contemporary Mathematics, vol. 558 (Model Theoretic Methods in Finite Combinatorics) (2011), 489–519.
[10] M., Bodirsky, M., Pinsker, and A., Pongrácz, The 42 reducts of the random ordered graph, 2013. Preprint arXiv:1309.2165.
[11] M., Bodirsky, M., Pinsker, and T., Tsankov, Decidability of definability, Journal of Symbolic Logic 78 (2013), no. 4, 1036–1054. A conference version appeared in the Proceedings of LICS 2011, pages 321–328.Google Scholar
[12] J., Böottcher and J., Foniok, Ramsey properties of permutations, Electronic Journal of Combinatorics 20 (2013), no. 1.Google Scholar
[13] P. J., Cameron, Transitivity of permutation groups on unordered sets, Mathematische Zeitschrift 148 (1976), 127–139.Google Scholar
[14] P. J., Cameron, Oligomorphic permutation groups, Cambridge University Press, Cambridge, 1990.
[15] P. J., Cameron, The random graph revisited, Proceedings of the european congress of mathematics, 2001, pp. 267–274.
[16] G., Cherlin and A. H., Lachlan, Stable finitely homogeneous structures, TAMS 296 (1986), 815–850.Google Scholar
[17] G., Cherlin, The classification of countable homogeneous directed graphs and countable homogeneous n-tournaments, AMS Memoir 131 (1998January), no. 621.Google Scholar
[18] W., Deuber, A generalization of Ramsey's theorem for regular trees, Journal of Combinatorial Theory, Series B 18 (1975), 18–23.Google Scholar
[19] J., Foniok, On ramsey properties of classes with forbidden trees, Logical Methods in Computer Science 10 (2014), no. 3.Google Scholar
[20] R., Fraïssé, Sur l'extension aux relations de quelques propriétées des ordres, Annales Scientifiques de l'École Normale Supéerieure 71 (1954), 363–388.Google Scholar
[21] R., Fraïssé, Theory of relations, Elsevier Science Ltd, North-Holland, 1986.
[22] R. L., Graham, B. L., Rothschild, and J. H., Spencer, Ramsey theory, Wiley-Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, Inc., New York, 1990. Second edition.
[23] Y., Gutman and L. N. V., Thé, Relative extreme amenability and interpolation, 2011. Preprint arXiv:1105.6221.
[24] W., Hodges, Model theory, Cambridge University Press, 1993.
[25] W., Hodges, A shorter model theory, Cambridge University Press, Cambridge, 1997.
[26] J., Hubička and J., Nešetřil, Bowtie-free graphs have a Ramsey lift, 2014. arXiv:1402.2700.
[27] A., Kechris, V., Pestov, and S., Todorcevic, Fraissé limits, Ramsey theory, and topological dynamics of automorphism groups, Geometric and Functional Analysis 15 (2005), no. 1, 106–189.Google Scholar
[28] A. S., Kechris, Dynamics of non-archimedean Polish groups, Proceedings of the european congress of mathematics, krakow, July 2, pp. 375–397.
[29] A. H., Lachlan, Countable homogeneous tournaments, TAMS 284 (1984), 431–461.Google Scholar
[30] A. H., Lachlan, Structures coordinatized by indiscernible sets, Annals of Pure and Applied Logic 34 (1987), 245–273.Google Scholar
[31] C., Laflamme, J., Jasinski, L. N. V., Thé, and R., Woodrow, Ramsey precompact expansions of homogeneous directed graphs (2013).
[32] K., Leeb, Vorlesungen öuber Pascaltheorie, Arbeitsberichte des Instituts föur Mathematische Maschinen und Datenverarbeitung, vol. 6, Friedrich-Alexander-Universitäat Erlangen-Nöurnberg, 1973.
[33] J., Linman and M., Pinsker, Permutations on the random permutation, 2014.
[34] J., Melleray, L. N. V., Thé, and T., Tsankov, Polish groups with metrizable universal minimal flows, 2014. Preprint arXiv:1404.6167.
[35] K. R., Milliken, A Ramsey theorem for trees, Journal of Combinatorial Theory, Series A 26 (1979), no. 3, 215–237.Google Scholar
[36] M., Müuller and A., Pongrácz, Topological dynamics of unordered ramsey structures, 2014. To appear in Fundamenta Mathematicae. ArXiv:1401.7766.
[37] J., Nešetřil, Ramsey theory, Handbook of Combinatorics (1995), 1331–1403.
[38] J., Nešetřil, Ramsey classes and homogeneous structures, Combinatorics, Probability & Computing 14 (2005), no. 1-2, 171–189.Google Scholar
[39] J., Nešetřil and V., Röodl, Ramsey classes of set systems, Journal of Combinatorial Theory, Series A 34 (1983), no. 2, 183–201.Google Scholar
[40] J., Nešetřil and V., Röodl, The partite construction and Ramsey set systems, Discrete Mathematics 75 (1989), no. 1-3, 327–334.Google Scholar
[41] J., Nešetřil and V., Röodl, Mathematics of Ramsey theory, Springer, Berlin, 1998.
[42] P. P., Pach, M., Pinsker, G., Pluhár, A., Pongrácz, and C., Szabó, Reducts of the random partial order, Advances in Mathematics 267 (2014), 94–120.Google Scholar
[43] A., Pongrácz, Reducts of the Henson graphs with a constant (2011). Preprint.
[44] H. J., Pröomel, Ramsey theory for discrete structures, Springer-Verlag, 2013.
[45] F. P., Ramsey, On a problem of formal logic, Proceedings of the LMS (2) 30 (1930), no. 1, 264–286.
[46] D., Saracino, Model companions for ℵ-categorical theories, Proceedings of the AMS 39 (1973), 591–598.
[47] M., Sokič, Ramsey property of posets and related structures, Ph.D. Thesis, 2010.
[48] M., Sokič, Ramsey property, ultrametric spaces, finite posets, and universal minimal flows, Israel Journal of Mathematics 194 (2013), no. 2, 609–640.Google Scholar
[49] M., Sokič, Directed graphs and Boron trees, 2015. Preprint available from http://www.its.caltech.edu/∼msokic/SAP3.pdf.
[50] L. N. V., Thé, More on the Kechris-Pestov-Todorcevic correspondence: precompact expansions, Fund. Math. 222 (2013), no. 1, 19–47. Preprint arXiv:1201.1270.
[51] L. N. V., Thé, Universal flows of closed subgroups of S∞ and relative extreme amenability, Asymptotic Geometric Analysis, Fields Institute Communications 68 (2013), 229–245.
[52] S., Thomas, Reducts of the random graph, Journal of Symbolic Logic 56 (1991), no. 1, 176–181.Google Scholar
[53] S., Thomas, Reducts of random hypergraphs, Annals of Pure and Applied Logic 80 (1996), no. 2, 165–193.Google Scholar
[54] A., Zucker, Amenability and unique ergodicity of automorphism groups of Fraissé structures, 2013. Preprint, arXiv:1304.2839.
[55] A., Zucker, Topological dynamics of closed subgroups of Sω, 2014. Preprint, arXiv:1404.5057.

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