Uncountable intersections of open sets under CPA
Authors:
Krzysztof Ciesielski and Janusz Pawlikowski
Journal:
Proc. Amer. Math. Soc. 132 (2004), 33793385
MSC (2000):
Primary 03E35; Secondary 03E17
Published electronically:
June 2, 2004
MathSciNet review:
2073315
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: We prove that the Covering Property Axiom CPA , which holds in the iterated perfect set model, implies the following facts. The example from the second fact refutes a conjecture of Brendle, Larson, and Todorcevic.
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K. Ciesielski, J. Pawlikowski, Small coverings with smooth functions under the Covering Property Axiom, Canad. J. Math., to appear. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.)
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K. Ciesielski, J. Pawlikowski, Covering Property Axiom CPA. A combinatorial core of the iterated perfect set model. To appear in Cambridge Tracts in Mathematics, Cambridge Univ. Press. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.)
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J. Zapletal, Cardinal Invariants and Descriptive Set Theory, Mem. Amer. Math. Soc. 167 (2004).
 1.
 J. Brendle, An email to J. Pawlikowski, June 11, 2000.
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 J. Brendle, P. Larson, S. Todorcevic, Rectangular axioms, perfect set properties and decomposition, preprint of November, 2002.
 3.
 K. Ciesielski, Set Theory for the Working Mathematician, London Math. Soc. Stud. Texts 39, Cambridge Univ. Press 1997. MR 99c:04001
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 K. Ciesielski, J. Pawlikowski, Crowded and selective ultrafilters under the Covering Property Axiom, J. Appl. Anal. 9(1) (2003), 1955. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.)
 5.
 K. Ciesielski, J. Pawlikowski, Small coverings with smooth functions under the Covering Property Axiom, Canad. J. Math., to appear. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.)
 6.
 K. Ciesielski, J. Pawlikowski, Covering Property Axiom CPA. A combinatorial core of the iterated perfect set model. To appear in Cambridge Tracts in Mathematics, Cambridge Univ. Press. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.)
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 K. Ciesielski, J. Pawlikowski, Covering Property Axiom CPA and its consequences, Fund. Math. 176(1) (2003), 6375. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.) MR 2004b:03076
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 V. Kanovei, NonGlimmEffros equivalence relations at second projective level, Fund. Math. 154 (1997), 135. MR 99j:03040
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 A. S. Kechris, Classical Descriptive Set Theory, SpringerVerlag, Berlin 1995. MR 96e:03057
 10.
 A. Nowik, Possibly there is no uniformly completely Ramsey null set of size , Colloq. Math. 93 (2002), 251258. (Preprint available in electronic form from Set Theoretic Analysis Web Page: http://www.math.wvu.edu/homepages/kcies/STA/STA.html.) MR 2003j:03057
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 J. Zapletal, Cardinal Invariants and Descriptive Set Theory, Mem. Amer. Math. Soc. 167 (2004).
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Additional Information
Krzysztof Ciesielski
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, West Virginia 265066310
Email:
K_Cies@math.wvu.edu
Janusz Pawlikowski
Affiliation:
Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50384 Wrocław, Poland
Email:
pawlikow@math.uni.wroc.pl
DOI:
http://dx.doi.org/10.1090/S0002993904074751
PII:
S 00029939(04)074751
Keywords:
Uncountable intersections of open sets.
Received by editor(s):
March 3, 2003
Received by editor(s) in revised form:
July 27, 2003
Published electronically:
June 2, 2004
Additional Notes:
The work of the first author was partially supported by NATO Grant PST.CLG.977652 and by a 2002/03 West Virginia University Senate Research Grant.
Communicated by:
Alan Dow
Article copyright:
© Copyright 2004
American Mathematical Society
