Miller, A. W., and Maxim R. Burke. “Models in Which Every Nonmeager Set Is Nonmeager in a Nowhere Dense Cantor Set”. Canadian Journal of Mathematics Journal Canadien De Mathematiques, vol. 57, no. 6, 2005, pp. 1139-54, https://doi.org/10.4153/cjm-2005-044-x.

Genre

  • Journal Article
Contributors
Author: Miller, A. W.
Author: Burke, Maxim R.
Date Issued
2005
Abstract

We prove that it is relatively consistent with ZFC that in any perfect Polish space, for every nonmeager set A there exists a nowhere dense Cantor set C such that A boolean AND C is nonmeager in C. We also examine variants of this result and establish a measure theoretic analog.

Note

Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE C1A 4P3, Canada. Univ Wisconsin, Dept Matemat, Madison, WI 53706 USA.; Burke, MR, Univ Prince Edward Isl, Dept Math & Stat, Charlottetown, PE C1A 4P3, Canada.; burke@upei.ca miller@math.wisc.edu

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CANADIAN MATHEMATICAL SOC

PT: J; CR: BAUMGARTNER J, 1983, LONDON MATH SOC LECT, V87, P1 BURKE M, 1993, ISRAEL MATH C P, V6, P119 CIESIELSKI K, 2000, J APPL ANAL, V6, P159 GOLDSTERN M, 1993, ISRAEL MATH C P, V6, P305 KUNEN K, 1983, SET THEORY PAWLIKOWSKI J, 1996, SET THEORY CONT MATH, V192, P71 ROSLANOWSKI A, MEASURED CREATURES SHELAH S, 1980, J SYMBOLIC LOGIC, V45, P563 SHELAH S, 1998, PROPER IMPROPER FORC; NR: 9; TC: 1; J9: CAN J MATH; PG: 16; GA: 985PA

Source type: Electronic(1)

Language

  • English

Subjects

  • Mathematics
  • property of Baire
  • oracle forcing
  • Lebesgue measure
  • Cantor set
Page range
1139-1154
Host Title
Canadian Journal of Mathematics / Journal Canadien De Mathematiques
Host Abbreviated Title
Can.J.Math.-J.Can.Math.
Volume
57
Issue
6
ISSN
0008-414X
DOI
https://doi.org/10.4153/cjm-2005-044-x

Department