Covering of the null ideal may have countable cofinality

Saharon Shelah

Fundamenta Mathematicae (2000)

  • Volume: 166, Issue: 1-2, page 109-136
  • ISSN: 0016-2736

Abstract

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We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.

How to cite

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Shelah, Saharon. "Covering of the null ideal may have countable cofinality." Fundamenta Mathematicae 166.1-2 (2000): 109-136. <http://eudml.org/doc/212472>.

@article{Shelah2000,
abstract = {We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.},
author = {Shelah, Saharon},
journal = {Fundamenta Mathematicae},
keywords = {null sets; cardinal invariants of the continuum; iterated forcing; ccc forcing; covering number; measure zero sets; cofinality},
language = {eng},
number = {1-2},
pages = {109-136},
title = {Covering of the null ideal may have countable cofinality},
url = {http://eudml.org/doc/212472},
volume = {166},
year = {2000},
}

TY - JOUR
AU - Shelah, Saharon
TI - Covering of the null ideal may have countable cofinality
JO - Fundamenta Mathematicae
PY - 2000
VL - 166
IS - 1-2
SP - 109
EP - 136
AB - We prove that it is consistent that the covering number of the ideal of measure zero sets has countable cofinality.
LA - eng
KW - null sets; cardinal invariants of the continuum; iterated forcing; ccc forcing; covering number; measure zero sets; cofinality
UR - http://eudml.org/doc/212472
ER -

References

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  1. [Ba88] T. Bartoszyński, On covering of real line by null sets, Pacific J. Math.,131 (1988), 1-12. Zbl0643.03034
  2. [BaJu95] T. Bartoszyński and H. Judah, Set Theory: On the Structure of the Real Line, A K Peters, Wellesley, MS, 1995. Zbl0834.04001
  3. [Fe94] D. Fremlin, Problem list, circulated notes, 1994. 
  4. [Ko] P. Komjáth, On second-category sets, Proc. Amer. Math. Soc. 107 (1989), 653-654. Zbl0672.28002
  5. [Mi82] A. W. Miller, A characterization of the least cardinal for which the Baire category theorem fails, Proc. Amer. Math. Soc. 86 (1982), 498-502. Zbl0506.03012
  6. [Sh 538] S. Shelah, Historic iteration with ℵ ε -support, Arch. Math. Logic, accepted. 
  7. [Sh 619] S. Shelah, The null ideal restricted to a non-null set may be saturated, preprint. Zbl1049.03038

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