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Ramsey games

1984
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Transactions of the American Mathematical Society
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The paper deals with game-theoretic versions of the partition relations a -» (ß)^T and a -> (ß)^ introduced in [2]. The main results are summarized in the Introduction. 0. Introduction. In their paper [2], Baumgartner, Galvin, McKenzie and Laver introduced a new game. Let a,ß be ordinals, r a cardinal. The Ramsey game Z?(a, r, ß) is defined as follows. There are two players, White and Black, who alternately pick previously unchosen members of [a]T. At limit stages it is of course White's turn

doi:10.1090/s0002-9947-1984-0743746-3
fatcat:vxh5vy2wonfeveddahwy4qiz7q