Happy families and completely Ramsey sets

Archive for Mathematical Logic 32 (3):151-171 (1993)
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Abstract

We use games of Kastanas to obtain a new characterization of the classC ℱ of all sets that are completely Ramsey with respect to a given happy family ℱ. We then combine this with ideas of Plewik to give a uniform proof of various results of Ellentuck, Louveau, Mathias and Milliken concerning the extent ofC ℱ. We also study some cardinals that can be associated with the ideal ℐℱ of nowhere ℱ-Ramsey sets

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10.1007/bf01375549

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Citations of this work

Combinatorics and forcing with distributive ideals.Pierre Matet - 1997 - Annals of Pure and Applied Logic 86 (2):137-201.
A generalization of the Dual Ellentuck Theorem.Lorenz Halbeisen & Pierre Matet - 2003 - Archive for Mathematical Logic 42 (2):103-128.

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References found in this work

Happy families.A. R. D. Mathias - 1977 - Annals of Mathematical Logic 12 (1):59.
Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
A new proof that analytic sets are Ramsey.Erik Ellentuck - 1974 - Journal of Symbolic Logic 39 (1):163-165.
Borel sets and Ramsey's theorem.Fred Galvin & Karel Prikry - 1973 - Journal of Symbolic Logic 38 (2):193-198.
Every analytic set is Ramsey.Jack Silver - 1970 - Journal of Symbolic Logic 35 (1):60-64.

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