Saturated families

Authors:
Martin Goldstern, Haim I. Judah and Saharon Shelah

Journal:
Proc. Amer. Math. Soc. **111** (1991), 1095-1104

MSC:
Primary 03E05; Secondary 54A25

DOI:
https://doi.org/10.1090/S0002-9939-1991-1052573-0

MathSciNet review:
1052573

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Abstract | References | Similar Articles | Additional Information

Abstract: We will show that implies that there exist saturated (or completely separable) almost disjoint families on sets of any infinite cardinality.

**[BDS]**B. Balcar, J. Dockalkova, and P. Simon,*Almost disjoint families of countable sets*, Finite and Infinite Sets, Proc. Coll. Math. Soc. J. Bolyai,**I**, Eger, 1981.**[EH1]**P. Erdős and A. Hajnal,*Unsolved problems in set theory*, 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. 17–48. MR**0280381****[EH2]**P. Erdős and A. Hajnal,*Unsolved and solved problems in set theory*, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1974, pp. 269–287. MR**0357122****[HJS]**A. Hajnal, I. Juhász, and L. Soukup,*On saturated almost disjoint families*, Comment. Math. Univ. Carolin.**28**(1987), no. 4, 629–633. MR**928677****[J]**Thomas Jech,*Set theory*, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR**506523****[K]**P. Komjath,*Dense systems of almost disjoint sets*, Finite and Infinite Sets, Proc. Coll. Math. Soc. J. Bolyai,**II**, Eger, 1981.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1052573-0

Keywords:
Almost disjoint families,
completely separable families,
saturated families

Article copyright:
© Copyright 1991
American Mathematical Society