Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On second-category sets


Author: P. Komjáth
Journal: Proc. Amer. Math. Soc. 107 (1989), 653-654
MSC: Primary 03E15; Secondary 03E55, 04A15, 28A12
DOI: https://doi.org/10.1090/S0002-9939-1989-0976358-7
MathSciNet review: 976358
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The existence of a measurable cardinal is equiconsistent to the existence of a second category set not decomposable into the union of uncountable many disjoint second category sets.


References [Enhancements On Off] (What's this?)

  • [1] D. H. Fremlin, Consequences of Martin's axiom, Cambridge Univ. Press, 1984.
  • [2] G. L. Itzkowitz, Continuous measures, Baire category, and uniform continuity in lopological groups, Pacific J. Math., 54 (1974), 1 15-125. MR 0372114 (51:8331)
  • [3] K. Kunen, Set theory, North-Holland, 1980. MR 597342 (82f:03001)
  • [4] -, Random and Cohen reals, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.) North-Holland, 1984, pp. 887-911. MR 776619 (85k:54001)
  • [5] K. Kuratowski, Topology I, Academic Press, 1966. MR 0217751 (36:840)
  • [6] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), 143-178. MR 0270904 (42:5787)
  • [7] J. C. Morgan II, Baire category from an abstract viewpoint, Fund. Math. 94 (1977), 13-23. MR 0433416 (55:6392)
  • [8] K. L. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. 68 (1970), 75-80. MR 0262075 (41:6685)
  • [9] W. Sierpiński, Hypothèse du continu, Chelsea Publ., New York, 1956. MR 0090558 (19:829c)
  • [10] R. M. Solovay, Real-valued measurable cardinals, Axiomatic Set Theory, (D. S. Scott, ed.) Amer. Math. Soc., Providence, R.I., 1971, pp. 397-428. MR 0290961 (45:55)
  • [11] S. Ulam, Über gewisse Zerlegungen von Mengen, Fund. Math. 20 (1933), 221-223.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E15, 03E55, 04A15, 28A12

Retrieve articles in all journals with MSC: 03E15, 03E55, 04A15, 28A12


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0976358-7
Article copyright: © Copyright 1989 American Mathematical Society

American Mathematical Society