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The Cichoń diagram

Published online by Cambridge University Press:  12 March 2014

Tomek Bartoszyński*
Affiliation:
Department of Mathematics, University of California, Berkeley, California94720
Haim Judah*
Affiliation:
Department of Mathematics, University of California, Berkeley, California94720 Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California94720
Saharon Shelah*
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey08903 Mathematical Sciences Research Institute, 1000 Centennial Drive, Berkeley, California94720
*
Department of Mathematics, Boise State University, Boise, Idaho 83725, E-mail: tomek@math.idbsu.ed
Department of Mathematics, Bar Ilan University, 52-100 Ramat Gan, Israel52900, E-mail: judah@bimacs.cs.biu.ac.il
Department of Mathematics, Hebrew University, Jerusalem, Israel, E-mail: shelah@sunrise.huji.ac.

Abstract

We conclude the discussion of additivity, Baire number, uniformity, and covering for measure and category by constructing the remaining 5 models. Thus we complete the analysis of Cichoń's diagram.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1993

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References

[1]Bartoszyński, T., Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), pp. 209213.CrossRefGoogle Scholar
[2]Blass, A. and Shelah, S., There may be simple - and -points and the Rudin-Keisler order may be downward directed, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 213243.CrossRefGoogle Scholar
[3]Baumgartner, J., Iterated forcing, Surveys in set theory, London Mathematical Society Lecture Note Series, no. 8, Cambridge University Press, Cambridge, 1983.Google Scholar
[4]Fremlin, D., On Cichoń's diagram, Initiation a l'Analyse, Universite Pierre et Marie Curie, Paris, 1985.Google Scholar
[5]Judah, H. and Shelah, S., The Kunen-Miller chart, this Journal, vol. 55 (1990), pp. 909927.Google Scholar
[6]Judah, H. and Shelah, S., sets, this Journal (to appear).Google Scholar
[7]Miller, A., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), pp. 93114.CrossRefGoogle Scholar
[8]Miller, A., Rational perfect set forcing, Axiomatic set theory (Baumgartner, James E., Martin, Donald A., and Shelah, Sharon, editors), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, Rhode Island, 1984, pp. 143159.CrossRefGoogle Scholar
[9]Shelah, S., Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin and New York, 1982.CrossRefGoogle Scholar
[10]Shelah, S., On cardinal invariants of the continuum, Axiomatic set theory (Baumgartner, James E., Martin, Donald A., and Shelah, Sharon, editors), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, Rhode Island, 1984, pp. 183207.CrossRefGoogle Scholar
[11]Shelah, S., Vive la difference, Set theory of the continuum, Springer-Verlag, Berlin, 1992, pp. 357406.CrossRefGoogle Scholar
[12]Shelah, S., Proper and improper forcing (to appear).Google Scholar
15
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