대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제33권3호
  • /
  • Pages.1001-1011
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  • 2018
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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REFINEMENT OF HOMOGENEITY AND RAMSEY NUMBERS

  • Kim, Hwajeong (Department of Mathematics Hannam University) ;
  • Lee, Gyesik (Department of Computer Science and Engineering Hankyong National University)
  • 투고 : 2017.06.03
  • 심사 : 2017.11.28
  • 발행 : 2018.07.31
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초록

We introduce some variants of the finite Ramsey theorem. The variants are based on a refinement of homogeneity. In particular, they cover homogeneity, minimal homogeneity, end-homogeneity as special cases. We also show how to obtain upper bounds for the corresponding Ramsey numbers.

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참고문헌

  1. L. Carlucci, G. Lee, and A. Weiermann, Sharp thresholds for hypergraph regressive Ramsey numbers, J. Combin. Theory Ser. A 118 (2011), no. 2, 558-585. https://doi.org/10.1016/j.jcta.2010.08.004
  2. D. Conlon, J. Fox, and B. Sudakov, Recent developments in graph Ramsey theory, in Surveys in combinatorics 2015, 49-118, London Math. Soc. Lecture Note Ser., 424, Cambridge Univ. Press, Cambridge, 2015.
  3. P. Erdos, Some remarks on the theory of graphs, Bull. Amer. Math. Soc. 53 (1947), 292-294. https://doi.org/10.1090/S0002-9904-1947-08785-1
  4. P. Erdos, A. Hajnal, A. Mate, and R. Rado, Combinatorial set theory: partition relations for cardinals, Studies in Logic and the Foundations of Mathematics, 106, North-Holland Publishing Co., Amsterdam, 1984.
  5. P. Erdos and R. Rado, Combinatorial theorems on classifications of subsets of a given set, Proc. London Math. Soc. (3) 2 (1952), 417-439.
  6. A. Freund, Proof lengths for instances of the Paris-Harrington principle, Ann. Pure Appl. Logic 168 (2017), no. 7, 1361-1382. https://doi.org/10.1016/j.apal.2017.01.004
  7. A. Kanamori and K. McAloon, On Godel incompleteness and finite combinatorics, Ann. Pure Appl. Logic 33 (1987), no. 1, 23-41. https://doi.org/10.1016/0168-0072(87)90074-1
  8. R. Kaye, Models of Peano Arithmetic, Oxford Logic Guides, 15, The Clarendon Press, Oxford University Press, New York, 1991.
  9. G. Lee, Phase Transitions in Axiomatic Thought, PhD thesis, University of Munster, May 2005.
  10. J. Paris and L. Harrington, A mathematical incompleteness in Peano arithmetic. I, J. Barwise, ed., Handbook of Mathematical Logic, volume 90 of Studies in Logic and the Foundations of Mathematics, pages 1133-1142. North-Holland, 1977.
  11. F. P. Ramsey, On a Problem of Formal Logic, Proc. London Math. Soc. (2) 30 (1929), no. 4, 264-286.
  12. A. Weiermann, A classification of rapidly growing Ramsey functions, Proc. Amer. Math. Soc. 132 (2004), no. 2, 553-561. https://doi.org/10.1090/S0002-9939-03-07086-2