Geodesic
Separating Points and Coloring Principles
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 398-404

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DOI

In 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.
DOI : 10.4153/CMB-1984-061-3
Mots-clés : 03E05, 54D15, 54A35, 03E35, 03E45 
Watson, W. Stephen. Separating Points and Coloring Principles. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 398-404. doi: 10.4153/CMB-1984-061-3
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     title = {Separating {Points} and {Coloring} {Principles}},
     journal = {Canadian mathematical bulletin},
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     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-061-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-061-3/}
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