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Almost Disjoint Families of Representing Sets
Author(s) -
Balanda Kevin P.
Publication year - 1985
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19850310108
Subject(s) - disjoint sets , citation , library science , media studies , sociology , computer science , mathematics , combinatorics
The thesis is concerned with a number of problems in Combinatorial Set Theory. The Generalized Continuum Hypothesis is assumed. Suppose X and K are non-zero cardinals. By successively identifying K with airwise disjoint sets of power K, a function/: X-*•K can be viewed as a transversal of a pairwise disjoint (X, K)family A . Questions about families of functions in K can thus bethought of as referring to families of transversals of A. We wish to consider generalizations of such questions to almost disjoint families; in particular we are interested in extensions of the following two problems:(i) What is the 'maximum' cardinality of an almost disjoint family of functions each mapping X into K?(ii) Describe the cardinalities of maximal almost disjoint families of functions each mapping X into K.Article in Bulletin of the Australian Mathematical Society 27(03):477 - 479 · June 1983