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Separating Points and Coloring Principles

Published online by Cambridge University Press:  20 November 2018

W. Stephen Watson
W. Stephen Watson*
Affiliation:
York University, DownsView, Ontario. M3J1P3, Canada
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Abstract

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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.

Keywords

03E0554D1554A3503E3503E45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 4 , 01 December 1984 , pp. 398 - 404
Copyright
Copyright © Canadian Mathematical Society 1984

Footnotes

This work has been supported by the Natural Sciences and Engineering Research Council of Canada.

References

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