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A topological reflection principle equivalent to Shelah's strong hypothesis
Author(s):
Assaf
Rinot
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4413-4416.
MSC (2000):
Primary 03E04;
Secondary 54G15, 03E65
Posted:
July 1, 2008
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Abstract:
We notice that Shelah's Strong Hypothesis is equivalent to the following reflection principle: Suppose  is a first-countable space whose density is a regular cardinal,  . If every separable subspace of  is of cardinality at most  , then the cardinality of  is  .
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Additional Information:
Assaf
Rinot
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Email:
assaf@rinot.com
DOI:
10.1090/S0002-9939-08-09411-2
PII:
S 0002-9939(08)09411-2
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
Posted:
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
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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