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A topological reflection principle equivalent to Shelah's strong hypothesis

Author: Assaf Rinot
Journal: Proc. Amer. Math. Soc. 136 (2008), 4413-4416
MSC (2000): Primary 03E04; Secondary 54G15, 03E65
Published electronically: July 1, 2008
MathSciNet review: 2431057
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Abstract: We notice that Shelah's Strong Hypothesis is equivalent to the following reflection principle:

Suppose $ \langle X,\tau\rangle$ is a first-countable space whose density is a regular cardinal, $ \kappa$. If every separable subspace of $ X$ is of cardinality at most $ \kappa$, then the cardinality of $ X$ is $ \kappa$.

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Additional Information

Assaf Rinot
Affiliation: School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Keywords: Shelah's Strong Hypothesis, first countable, countably tight.
Received by editor(s): September 28, 2007
Received by editor(s) in revised form: November 3, 2007
Published electronically: July 1, 2008
Additional Notes: The author would like to thank his Ph.D. advisor, M. Gitik, for his comments and remarks.
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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