Download PDF - Towers of measurable functionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Towers of measurable functions

Authors 1

Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, Ontario

Abstract

We formulate variants of the cardinals f, p and t in terms of families of measurable functions, in order to examine the effect upon these cardinals of adding one random real.

Bibliography

  1. [Abr80] F. G. Abramson, A simplicity theorem for amoebas over random reals, Proc. Amer. Math. Soc. 78 (1980), 409-413.
  2. [BD85] J. E. Baumgartner and P. Dordal, Adjoining dominating functions, J. Symbolic Logic 50 (1985), 94-101.
  3. [Bel81] M. G. Bell, On the combinatorial principle P(c), Fund. Math. 114 (1981), 149-157.
  4. [BJ95] T. Bartoszyński and H. Judah, Set Theory. On the Structure of the Real Line, A. K. Peters, Wellesley, MA, 1995.
  5. [Bla99] A. Blass, Combinatorial cardinal characteristics of the continuum, to appear.
  6. [BRS96] T. Bartoszyński, A. Rosłanowski and S. Shelah, Adding one random real, J. Symbolic Logic 61 (1996), 80-90.
  7. [BS96] J. Brendle and S. Shelah, Evasion and prediction. II, J. London Math. Soc. (2) 53 (1996), 19-27.
  8. [vD84] E. K. van Douwen, The integers and topology, in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 111-167.
  9. [Hir00] J. Hirschorn, Towers of Borel functions, Proc. Amer. Math. Soc. 128 (2000), 599-604.
  10. [Laf97] C. Laflamme, Combinatorial aspects of Fσ filters with an application to N-sets, Proc. Amer. Math. Soc. 125 (1997), 3019-3025.
  11. [PS87] Z. Piotrowski and A. Szymański, Some remarks on category in topological spaces, ibid. 101 (1987), 156-160.
  12. [Roi79] J. Roitman, Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom, Fund. Math. 103 (1979), 47-60.
  13. [Roi79] J. Roitman, Correction to: "Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom", ibid. 129 (1988), 141.
  14. [Roy88] H. L. Royden, Real Analysis, third ed., Macmillan, New York, 1988.
  15. [Sco67] D. Scott, A proof of the independence of the continuum hypothesis, Math. Systems Theory 1 (1967), 89-111.
  16. [Vau90] J. E. Vaughan, Small uncountable cardinals and topology, with an appendix by S. Shelah, in: Open Problems in Topology, North-Holland, Amsterdam, 1990, 195-218.
Fundamenta Mathematicae
2000/164/2
Export to PBN, Opens in new tab
Pages:
165-192
Main language of publication
English
Received
1999-09-05
Accepted
2000-02-22
Published
2000
Exact and natural sciences