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Refinement of Homogeneity and Ramsey numbers

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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.

Abstract

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.

참고문헌 (12)

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  9. G. Lee, "Phase Transitions in Axiomatic Thought", PhD, pp.2005
  10. J. Paris, "Handbook of Mathematical Logic, volume 90 of Studies in Logic and the Foundations of Mathematics", pp.1133~1142 (1977), North-Holland
  11. F. P. Ramsey, "On a Problem of Formal Logic", Proc. London Math. Soc. (2), 30(4), pp.264~286 (1929)
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