Luzin and anti-Luzin almost disjoint families

• Autorzy: Judith Roitman , Lajos Soukup
• Języki publikacji: EN

Abstrakty

EN

Under $MA_{ω_1}$ every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.

Słowa kluczowe

EN

Luzin; almost disjoint family

Kategorie tematyczne

• 03E25: Axiom of choice and related propositions
• 54G20: Counterexamples
• 06E99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 1
• Strony: 51-67

Daty

wydano

1998

otrzymano

1997-07-24

Twórcy

autor

Judith Roitman

• Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, U.S.A.

autor

Lajos Soukup

• Institute, Hungarian Academy of Sciences, POB 127, H-1364 Budapest, Hungary

Bibliografia

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• [HJ] A. Hajnal and I. Juhász, Intersection properties of open sets, ibid. 19 (1985), 201-209.
• [JN] I. Juhász, Zs. Nagy, L. Soukup and Z. Szentmiklóssy, Intersection properties of open sets, II, in: Papers on General Topology and Applications, Proc. 10th Summer Conference in General Topology and Applications, 1994, E. Coplakova and K. P. Hart (eds.), Ann. New York Acad. Sci. 788, New York Acad. Sci., 1996, 147-159.
• [JS] I. Juhász, L. Soukup and Z. Szentmiklóssy, Combinatorial principles from adding Cohen reals, in: Logic Colloquium 95, Haifa, to appear.
• [K] S. Koppelberg, Handbook of Boolean Algebras, Vol. I, North-Holland, Amsterdam, 1987.
• [L] N. Luzin, On parts of the natural series, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), 403-410 (in Russian).
• [V] B. Velickovic, OCA and automorphisms of P(ω)/fin, Topology Appl. 49 (1993), 1-13.