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The Cichoń diagram

  • Tomek Bartoszyński (a1), Haim Judah (a1) (a2) and Saharon Shelah (a3) (a2)
Abstract
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.

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Corresponding author
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.
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[1] T. Bartoszyński , Additivity of measure implies additivity of category, Transactions of the American Mathematical Society, vol. 281 (1984), pp. 209213.

[2] A. Blass and S. Shelah , 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.

[3] J. Baumgartner , Iterated forcing, Surveys in set theory, London Mathematical Society Lecture Note Series, no. 8, Cambridge University Press, Cambridge, 1983.

[7] A. Miller , Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), pp. 93114.

[8] A. Miller , Rational perfect set forcing, Axiomatic set theory ( James E. Baumgartner , Donald A. Martin , and Sharon Shelah , editors), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, Rhode Island, 1984, pp. 143159.

[9] S. Shelah , Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin and New York, 1982.

[10] S. Shelah , On cardinal invariants of the continuum, Axiomatic set theory ( James E. Baumgartner , Donald A. Martin , and Sharon Shelah , editors), Contemporary Mathematics, vol. 31, American Mathematical Society, Providence, Rhode Island, 1984, pp. 183207.

[11] S. Shelah , Vive la difference, Set theory of the continuum, Springer-Verlag, Berlin, 1992, pp. 357406.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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