Abstract
There is a gap between the infinite Ramsey’s theorem ω → (ω) n k and its finite version
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References
Alon, N., Füredi, Z., Katchalski, M. (1985): Separating pairs of points by standard boxes. Europ. J. Combinatorics 6, 205–210
Balcar, B., Stëpânek, P. (1986): Set theory. Academia Praha, Prague (In Czech)
Chvâtal, V. (1977): Tree-complete graph Ramsey numbers. J. Graph Theory 1, 93
Dilworth, R.P. (1950): A decomposition theorem for partially ordered sets. Ann. Math., II. Ser. 51, 161–166
Erdös, P., Szekeres, G. (1935): A combinatorial problem in geometry. Compos. Math. 2, 463–470
Erdös, P., Rado, R. (1950): A combinatorial theorem. J. Lond. Math. Soc. 25, 249–255
Erdös, P., Graham, R.L. (1980): Old and new problems and results in combinatorial number theory. L’Enseignement Mathématique, Université de Genève, Geneva (Monogr. Enseign. Math., Vol. 28)
Graham, R.L., Rothschild, B., Spencer, J. (1980): Ramsey theory. J. Wiley & Sons, New York, NY
Higman, G. (1952): Ordering by divisibility in abstract algebras. Proc. Lond. Math. Soc., III. Ser. 2, 326–336
de Jongh, D.H.J., Parikh, R. (1977): Well-partial orderings and hierarchies. Proc. K. Ned. Akad. Wet., Ser. A 80 (Indagationes Math. 39), 195–207
Kříž, I.: On perfect lattices. (To appear)
Kruskal, J. (1960): Well-quasi-ordering, the tree-theorem, and Vazsonyi’s conjecture. Trans. Am. Math. Soc. 95, 210–225
Kruskal, J. (1972): The theory of well-quasi-ordering: a frequently discovered concept. J. Comb. Theory, Ser. A 13, 297–305
Milner, E.C., Sauer, N.: On chains and antichains in well-founded partially ordered sets. Preprint
Nash-Williams, C.St.J.A. (1963): On well-quasi-ordering finite trees. Proc. Camb. Philos. Soc. 59, 833–835
Nash-Williams, C.St.J.A. (1965): On well-quasi-ordering transfinite sequences. Proc. Camb. Philos. Soc. 61, 33–39
Nešetřil, J., Rödl, V. (1979): Partition theory and its application. In: Bollobâs, B. (ed.): Surveys in combinatorics. Cambridge University Press, Cambridge, pp. 96–156 (Lond. Math. Soc. Lect. Note Ser., Vol. 38)
Nešetřil, J. (1987): Ramsey theory. In: Graham, R.L., Grötschel, M., Lovâsz, L. (eds.): Handbook of combinatorics. (To appear)
Ore, O. (1962): Theory of graphs. American Mathematical Society, Providence, RI
Paris, J.B., Harrington, L.A. (1977): A mathematical incompleteness in Peano arithmetic. In: Barwise, J. (ed.): Handbook of mathematical logic. North Holland, Amsterdam, pp. 1133–1142 (Stud. Logic Found. Math., Vol. 90)
Pouzet, M. (1979): Sur les chaînes d’un ensemble partiellement bien ordonné. Publ. Dép. Math., Nouv. Ser., Univ. Claude Bernard, Lyon 16, 21–26
Pudlák, P., Rödl, V. (1982): Partition theorems for systems of finite subsets of integers. Discrete Math. 39, 67–73
Robertson, N., Seymour, P.D.: Graph minors I-XVIII.
Schmidt, D. (1978): Associative ordinal functions, well partial orderings and a problem of Skolem. Z. Math. Logik Grundlagen Math. 24, 297–302
Schmidt, D. (1979): Well partial orderings and their maximal order types. Inaugural Dissertation, Universität Heidelberg
Schmidt, D. (1981): The relation between the height of a well-founded partial ordering and the order types of its chains and antichains. J. Comb. Theory, Ser. B 31, 183–189
Schütte, K., Simpson, S.G. (1985): Ein in der reinen Zahlentheorie unbeweisbarer Satz über endliche Folgen von natürlichen Zahlen. Arch. Math. Logik Grundlagenforsch. 25, 75–89
Simpson, S.G. (1985): Nonprovability of certain combinatorial properties of finite trees. In: Harrington, L.A., Morley, M.D., Scedrov, A., Simpson, S.G. (eds.): Harvey Friedman’s research on the foundations of mathematics. North Holland, Amsterdam, pp. 87–117 (Stud. Logic Found. Math., Vol. 117)
Wolk, E.S. (1967): Partially well ordered sets and partial ordinals. Fundam. Math. 60, 175–186
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Kříž, I., Thomas, R. (1990). Ordinal Types in Ramsey Theory and Well-Partial-Ordering Theory. In: Nešetřil, J., Rödl, V. (eds) Mathematics of Ramsey Theory. Algorithms and Combinatorics, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72905-8_7
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