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First countable, countably compact spaces and the continuum hypothesis
Author(s):
Todd
Eisworth;
Peter
Nyikos
Journal:
Trans. Amer. Math. Soc.
357
(2005),
4269-4299.
MSC (2000):
Primary 03E75
Posted:
June 21, 2005
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Abstract:
We build a model of ZFC+CH in which every first countable, countably compact space is either compact or contains a homeomorphic copy of  with the order topology. The majority of the paper consists of developing forcing technology that allows us to conclude that our iteration adds no reals. Our results generalize Saharon Shelah's iteration theorems appearing in Chapters V and VIII of Proper and improper forcing (1998), as well as Eisworth and Roitman's (1999) iteration theorem. We close the paper with a ZFC example (constructed using Shelah's club-guessing sequences) that shows similar results do not hold for closed pre-images of  .
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Additional Information:
Todd
Eisworth
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, Iowa 50613
Address at time of publication:
Department of Mathematics, Ohio University, Athens, Ohio 45701
Email:
eisworth@uni.edu, eisworth@math.ohiou.edu
Peter
Nyikos
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Email:
nyikos@math.sc.edu
DOI:
10.1090/S0002-9947-05-04034-1
PII:
S 0002-9947(05)04034-1
Keywords:
Proper forcing,
iterations,
Continuum Hypothesis,
pre--images of $\omega_1$
Received by editor(s):
May 23, 2002
Posted:
June 21, 2005
Additional Notes:
The first author was partially supported by a Summer Fellowship granted by the Graduate College of the University of Northern Iowa
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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