Separating Points and Coloring Principles
AbstractIn the mid 1970's, Shelah formulated a weak version of ◊. This axiom Φ is a prediction principle for colorings of the binary tree of height ω1. Shelah and Devlin showed that Φ is equivalent to 2ℵ0 < 2ℵ1.In this paper, we formulate Φp, a "Φ for partial colorings", show that both ◊* and Fleissner's “◊ for stationary systems” imply Φp, that ◊ does not imply Φp and that Φp does not imply CH.We show that Φp implies that, in a normal first countable space, a discrete family of points of cardinality ℵ1 is separated.
1977 ◽
Vol 18
(2)
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pp. 199-207
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2006 ◽
Vol 153
(18)
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pp. 3420-3429
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1999 ◽
Vol 22
(3)
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pp. 659-665
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