Abstract
Using topological concepts A. Blass [1] proved an uncountable version of Ramsey’s theorem. Here we prove a canonical version of this result.
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References
A. Blass, A partition theorem for perfect sets, Proc. Amer. Math. Soc., 82 (1981) 271–277.
J.P. Burgess, A selector principle for \( {m_{1} {1}} \) equivalence relations, Michigan Math. J. 24 (1977) 65–76.
A. Emerik, R. Frankiewicz and W. Kulpa, On functions having the Baire-property, Bull. Acad. Polon. Math., 27 (1979) 489–491.
P. Erdős and R. Rado, A combinatorial theorem, J. London Math. Soc. 25 (1950) 249–255.
P. Erdős and R. Rado, Combinatorial theorems on classification of subsets of a given set, Proc. London Math. Soc. 3 (1952) 417–439.
F. Galvin, Partition theorems for the real line, Notices Amer. Math. Soc. 15 (1968) 660; Errata: Notices Amer. Math. Soc. 16 (1969) 1095.
K. Kuratowski, Topology I, Academic Press, 1966, New York.
J. Mychielsky, Independent sets in topological algebras, Fund. Math. 55 (1964) 139–147.
H.J. Prömel, S.G. Simpson and B. Voigt, A dual form of Erdős-Rado’s canonizing theorem, J. Comb. Theory Ser. A 42, (1986) 159–178.
H.J. Prömel and B. Voigt, Canonizing Ramsey Theory, preprint, Bielefeld, 1985.
F.P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1930), 264–286.
A.D. Taylor, Partitions of pairs of reals, Fund. Math. 99 (1979) 51–59.
B. Voigt, Canonizing partition theorems: diversifications, products and iterated versions, J. Comb. Th. Ser. A 40 (1985) 349–376.
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© 1989 Springer-Verlag Berlin Heidelberg
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Lefmann, H. (1989). Canonical Partition Behaviour of Cantor Spaces. In: Halász, G., Sós, V.T. (eds) Irregularities of Partitions. Algorithms and Combinatorics 8, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61324-1_8
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DOI: https://doi.org/10.1007/978-3-642-61324-1_8
Publisher Name: Springer, Berlin, Heidelberg
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