Property C'', strong measure zero sets and subsets of the plane

• Autorzy: Janusz Pawlikowski
• Języki publikacji: EN

Abstrakty

EN

Let X be a set of reals. We show that
 • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections $F_x$ (x ∈ X) null, $∪_{x ∈ X}F_x$ is null;
 • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections $F_x$ (x ∈ ℝ) null, $∪_{x ∈ X}F_x$ is null.

Kategorie tematyczne

• 03E15: Descriptive set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1997
• Tom: 153
• Numer: 3
• Strony: 277-293

Daty

wydano

1997

otrzymano

1996-09-04

poprawiono

1997-03-01

Twórcy

autor

Janusz Pawlikowski

• Department of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [AR] A. Andryszczak and I. Recław, A note on strong measure zero sets, Acta Univ. Carolin. Math. Phys. 34 (2) (1993), 7-9.
• [BS] T. Bartoszyński and S. Shelah, Closed measure zero sets, Ann. Pure Appl. Logic 58 (1992), 93-110.
• [D] C. Dellacherie, Un cours sur les ensembles analytiques, in: Analytic Sets, C. A. Rogers et al. (eds.), Academic Press, 1980, 183-316.
• [FM] D. H. Fremlin and A. Miller, On some properties of Hurewicz, Menger and Rothberger, Fund. Math. 129 (1988), 17-33.
• [G] F. Galvin, Indeterminacy of point-open games, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 445-449.
• [GMS] F. Galvin, J. Mycielski and R. M. Solovay, Strong measure zero sets, Notices Amer. Math. Soc. 26 (1979), A-280.
• [Ke] A. S. Kechris, Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer, 1995.
• [M] A. W. Miller, Special subsets of the real line, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 201-233.
• [M1] A. W. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114, and 271 (1982), 347-348.
• [P] J. Pawlikowski, Undetermined sets of point-open games, Fund. Math. 144 (1994), 279-285.
• [P1] J. Pawlikowski, A characterization of strong measure zero sets, Israel J. Math. 93 (1996), 171-184.
• [R] I. Recław, Every Lusin set is undetermined in the point-open game, Fund. Math. 144 (1994), 43-54.
• [Sh] S. Shelah, Vive la différence I: Nonisomorphism of ultrapowers of countable models, in: Set Theory of the Continuum, H. Judah, W. Just and H. Woodin (eds.), Springer, 1992, 357-405.
• [T] J. Truss, Sets having calibre $ℵ_1$, in: Logic Colloquium '76, R. Gandy and M. Hyland (eds.), Stud. Logic Found. Math. 87, North-Holland, 1977, 595-612.