Determinateness and partitions

Karel Prikry

doi:10.1090/S0002-9939-1976-0453540-X

Determinateness and partitions

Karel Prikry

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

It is proved that the axiom of determinateness of Mycielski and Steinhaus for games in which players alternate in writing reals implies that ω → (ω)^ω₂ (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).

Original language	English (US)
Pages (from-to)	303-306
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	54
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1976-0453540-X
State	Published - Jan 1976

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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 ω → (ω)ω2 (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).",

author = "Karel Prikry",

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AB - It is proved that the axiom of determinateness of Mycielski and Steinhaus for games in which players alternate in writing reals implies that ω → (ω)ω2 (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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