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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Determinateness and partitions


Author: Karel Prikry
Journal: Proc. Amer. Math. Soc. 54 (1976), 303-306
MSC: Primary 04A20; Secondary 04A25
DOI: https://doi.org/10.1090/S0002-9939-1976-0453540-X
MathSciNet review: 0453540
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Abstract: It is proved that the axiom of determinateness of Mycielski and Steinhaus for games in which players alternate in writing reals implies that $ \omega \to (\omega )_2^\omega $ (i.e. for every partition of infinite sets of natural numbers into two classes there is an infinite set such that all its infinite subsets belong to the same class).


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DOI: https://doi.org/10.1090/S0002-9939-1976-0453540-X
Article copyright: © Copyright 1976 American Mathematical Society