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
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] Gerald L. Itzkowitz, Continuous measures, Baire category, and uniform continuity in topological groups, Pacific J. Math. 54 (1974), no. 2, 115–125. MR 0372114
  • [3] Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
  • [4] Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland Publishing Co., Amsterdam, 1984. MR 776619
  • [5] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. MR 0217751
  • [6] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 0270904,
  • [7] John C. Morgan II, Baire category from an abstract viewpoint, Fund. Math. 94 (1977), no. 1, 13–23. MR 0433416
  • [8] K. L. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. Rozprawy Mat. 68 (1970), 55. MR 0262075
  • [9] Wacław Sierpiński, Hypothèse du continu, Chelsea Publishing Company, New York, N. Y., 1956 (French). 2nd ed. MR 0090558
  • [10] Robert M. Solovay, Real-valued measurable cardinals, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1971, pp. 397–428. MR 0290961
  • [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

Article copyright: © Copyright 1989 American Mathematical Society