Towers of measurable functions

James Hirschorn

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 2, page 165-192
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Hirschorn, James. "Towers of measurable functions." Fundamenta Mathematicae 164.2 (2000): 165-192. <http://eudml.org/doc/212452>.

@article{Hirschorn2000,
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.},
author = {Hirschorn, James},
journal = {Fundamenta Mathematicae},
keywords = {small cardinals; measurable functions; random real},
language = {eng},
number = {2},
pages = {165-192},
title = {Towers of measurable functions},
url = {http://eudml.org/doc/212452},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Hirschorn, James
TI - Towers of measurable functions
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 2
SP - 165
EP - 192
AB - 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.
LA - eng
KW - small cardinals; measurable functions; random real
UR - http://eudml.org/doc/212452
ER -

References

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  1. [Abr80] F. G. Abramson, A simplicity theorem for amoebas over random reals, Proc. Amer. Math. Soc. 78 (1980), 409-413. Zbl0446.03040
  2. [BD85] J. E. Baumgartner and P. Dordal, Adjoining dominating functions, J. Symbolic Logic 50 (1985), 94-101. Zbl0566.03031
  3. [Bel81] M. G. Bell, On the combinatorial principle P(c), Fund. Math. 114 (1981), 149-157. Zbl0581.03038
  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. Zbl0859.03023
  7. [BS96] J. Brendle and S. Shelah, Evasion and prediction. II, J. London Math. Soc. (2) 53 (1996), 19-27. Zbl0854.03045
  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. Zbl0933.03054
  10. [Laf97] C. Laflamme, Combinatorial aspects of F σ filters with an application to N-sets, Proc. Amer. Math. Soc. 125 (1997), 3019-3025. Zbl0883.04004
  11. [PS87] Z. Piotrowski and A. Szymański, Some remarks on category in topological spaces, ibid. 101 (1987), 156-160. Zbl0634.54002
  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. Zbl0442.03034
  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. Zbl0657.03037
  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. Zbl0149.25302
  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. 

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