Measurable cardinals and category bases

Andrzej Szymański

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 2, page 405-409
  • ISSN: 0010-2628

Abstract

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We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.

How to cite

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Szymański, Andrzej. "Measurable cardinals and category bases." Commentationes Mathematicae Universitatis Carolinae 32.2 (1991): 405-409. <http://eudml.org/doc/247256>.

@article{Szymański1991,
abstract = {We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.},
author = {Szymański, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {category base; precipitous ideal; measurable cardinal; precipitous ideal; category decomposition; Baire property; category base; measurable cardinal},
language = {eng},
number = {2},
pages = {405-409},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Measurable cardinals and category bases},
url = {http://eudml.org/doc/247256},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Szymański, Andrzej
TI - Measurable cardinals and category bases
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 2
SP - 405
EP - 409
AB - We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
LA - eng
KW - category base; precipitous ideal; measurable cardinal; precipitous ideal; category decomposition; Baire property; category base; measurable cardinal
UR - http://eudml.org/doc/247256
ER -

References

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  1. Jech T., Set Theory, Academic Press, 1978. Zbl1007.03002MR0506523
  2. Jech T., Magidor M., Mitchell W., Prikry K., Precipitous ideals, Journal of Symbolic Logic 45 1-8. Zbl0437.03026MR0560220
  3. Kunen K., Szymański A., Tall F., Baire irresolvable spaces and ideal theory, Acta Math. Silesiana, No. 14 (1986), 98-107. (1986) MR0861505
  4. Morgan J.C.II, Point Set Theory, Marcel Dekker, Inc., 1990. Zbl0937.26519MR1026014
  5. Solovay R., Real valued measurable cardinals, in Axiomatic Set Theory, Proc. Symp. Pure Math. 13.1 (D. Scott ed.), 397-428, Amer. Math. Soc., 1971. Zbl0222.02078MR0290961

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