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Separating Points and Coloring Principles

  • W. Stephen Watson (a1)

Abstract

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 20 < 21 .

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.

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Copyright

References

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1. Devlin, K. and Shelah, S., A weak version of ◊ which follows from 20 < 21 , Israel Journal of Math 29 (1978) 239-247.
2. Fleissner, W. G., Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974) 294-298.
3. Mathias, A. R. D., Logic Colloquium 76, North Holland 1977, p. 542.
4. Shelah, S., S. A Note in General Topology; If then any normal space is ℵ1-CWH; Preprints in Math. Logic, spring 1979.
5. Shelah, S., Whitehead Groups may not be free, even assuming CH, Israel Journal of Math. I 28 (1977) 193-204; II 35 (1980) 257–285.
6. Taylor, A. D., Diamond Principles, Ideals and the Normal Moore Space Problem. Can. Jour. Math. 33 (1981) 282-296.
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Separating Points and Coloring Principles

  • W. Stephen Watson (a1)

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