Saturated families
Authors:
Martin Goldstern, Haim I. Judah and Saharon Shelah
Journal:
Proc. Amer. Math. Soc. 111 (1991), 10951104
MSC:
Primary 03E05; Secondary 54A25
MathSciNet review:
1052573
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Abstract 
References 
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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
(43 #6101)
 [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
(50 #9590)
 [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
(89b:03079)
 [J]
Thomas
Jech, Set theory, Academic Press [Harcourt Brace Jovanovich,
Publishers], New YorkLondon, 1978. Pure and Applied Mathematics. MR 506523
(80a:03062)
 [K]
P. Komjath, Dense systems of almost disjoint sets, Finite and Infinite Sets, Proc. Coll. Math. Soc. J. Bolyai, II, Eger, 1981.
 [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. Erdös and A. Hajnal, Unsolved problems in set theory, Proc. Sympos. Pure Math. 13 (1971), 1748. MR 0280381 (43:6101)
 [EH2]
 , Unsolved and solved problems in set theory, Proc. Sympos. Pure Math. 25 (1971), 269287. MR 0357122 (50:9590)
 [HJS]
 A. Hajnal, I. Juhász and L. Soukup, On saturated almost disjoint families, Comment. Math. Univ. Carolina 28 (1987). MR 928677 (89b:03079)
 [J]
 T. Jech, Set theory, Academic Press, New York, San Francisco, and London, 1978. MR 506523 (80a:03062)
 [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:
http://dx.doi.org/10.1090/S00029939199110525730
PII:
S 00029939(1991)10525730
Keywords:
Almost disjoint families,
completely separable families,
saturated families
Article copyright:
© Copyright 1991
American Mathematical Society
