On the Blackwell property of Luzin sets
HTML articles powered by AMS MathViewer
- by Jakub Jasiński PDF
- Proc. Amer. Math. Soc. 95 (1985), 303-306 Request permission
Abstract:
We prove under the CH (Continuum Hypothesis) that there are strongly Blackwell Luzin sets and not Blackwell Luzin sets. We also indicate how these results can be generalized under MA (Martin’s Axiom).References
- K. P. S. Bhaskara Rao and B. V. Rao, Borel spaces, Dissertationes Math. (Rozprawy Mat.) 190 (1981), 63. MR 634451
- Gustave Choquet, Topology, Pure and Applied Mathematics, Vol. XIX, Academic Press, New York-London, 1966. Translated from the French by Amiel Feinstein. MR 0193605 E. Marczewski, O zbiorach i funkcjach bezwzglednie mierzalnych, Odbitka ze sprawozdań z posiedzeń Towarzystwa Naukowego Warszawskiego 30 (1937), Wydzial III, 1-30 (English transl. by J. C. Morgan is available in manuscript). —, , The characteristic function of the sequence of sets and some of its applications, Fund. Math. 31 (1938), 207-223.
- D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4
- M. Orkin, A Blackwell space which is not analytic, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 20 (1972), 437–438 (English, with Russian summary). MR 316655
- John C. Oxtoby, Measure and category, 2nd ed., Graduate Texts in Mathematics, vol. 2, Springer-Verlag, New York-Berlin, 1980. A survey of the analogies between topological and measure spaces. MR 584443, DOI 10.1007/978-1-4684-9339-9
- 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
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 95 (1985), 303-306
- MSC: Primary 28A05; Secondary 03E15, 04A15
- DOI: https://doi.org/10.1090/S0002-9939-1985-0801343-1
- MathSciNet review: 801343