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Essentially unbounded chains in compact sets

Published online by Cambridge University Press:  24 October 2008

D. H. Fremlin  and
K. Kunen
D. H. Fremlin
Affiliation:
Mathematics Department, University of Essex, Colchester C04 3SQ, England
K. Kunen
Affiliation:
Mathematics Department, Van Vleck Hall, University of Wisconsin, Madison, WI 53706, U.S.A.
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Extract

We discuss the possible cofinalities of ⊆ *-chains in ℕ which are ⊆ *-unbounded in their topological closures.

1. The problem. Throughout this paper, the power set ℕ of the set ℕ of natural numbers will be given its usual compact metrizable topology corresponding to the product topology of {0,1}N. We say that a ⊆ * b if a/b is finite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 109 , Issue 1 , January 1991 , pp. 149 - 160
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Bartoszyński, T.. Additivity of measure implies additivity of category. Trans. Amer. Math. Soc. 281 (1984), 209–213.Google Scholar
[2]Baumgartner, J. E.. Applications of the proper forcing axiom (pp. 913–960 in [10]).CrossRefGoogle Scholar
[3]van Douwen, E. K.. The integers and topology (pp. 111–168 in [10]).Google Scholar
[4]Fremlin, D. H.. Consequences of Martin's Axiom (Cambridge University Press, 1984).CrossRefGoogle Scholar
[5]Fremlin, D. H.. Cichoń's Diagram. Séminaire d'initiation à l'analyse (Choquet, G., Rogalski, M., Saint-Raymond, J.), Univ. Pierre et Marie Curie, Paris 23 (1985), 5.01–5.13.Google Scholar
[6]Fremlin, D. H.. Measure Algebras (pp. 878–980 in [11]).Google Scholar
[7]Hausdorff, F.. Summen von ℵ1 Mengen. Fund. Math. 26 (1936), 241–255.CrossRefGoogle Scholar
[8]Kunen, K.. Inaccessibility properties of cardinals. Ph.D. thesis, Stanford University (1968).Google Scholar
[9]Kunen, K.. Set Theory (North-Holland, 1980).Google Scholar
[10]Kenun, K. and Vaughan, J. E. (editors). Handbook of Set-Theoretic Topology (North-Holland, 1984).Google Scholar
[11]Monk, J. D. (editor). Handbook of Boolean Algebra (North-Holland, 1989).Google Scholar
[12]Scott, D. S. (editor). Axiomatic Set Theory. (Proc. Symposia Pure Math. vol. 13, American Mathematical Society, 1971).Google Scholar
[13]Solovay, R. M.. Real-valued measurable cardinals (pp. 397–428 in [12]).Google Scholar
[14]Weiss, W.. Versions of Martin's Axiom (pp. 827–886 in [10]).CrossRefGoogle Scholar