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Cardinal Invariants and Eventually Different Functions

Cardinal Invariants and Eventually Different Functions In this paper we study several kinds of maximal almost disjoint families. In the main result of this paper we show that for successor cardinals κ, there is an unexpected connection between invariants ae(κ), b(κ) and a certain cardinal invariant md(κ+) on κ+. As a corollary we get for example the following result. For a successor cardinal κ, even assuming that κ<κ = κ and 2κ = κ+, the following is not provable in Zermelo–Fraenkel set theory. There is a κ+‐cc poset which does not collapse κ and which forces a(κ) = κ+ < ae(κ) = κ++ = 2κ. We also apply the ideas from the proofs of these results to study a = a(ω) and non(M). 2000 Mathematics Subject Classification 03E17 (primary), 03E05 (secondary). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Cardinal Invariants and Eventually Different Functions

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References (9)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/S002460930501831X
Publisher site
See Article on Publisher Site

Abstract

In this paper we study several kinds of maximal almost disjoint families. In the main result of this paper we show that for successor cardinals κ, there is an unexpected connection between invariants ae(κ), b(κ) and a certain cardinal invariant md(κ+) on κ+. As a corollary we get for example the following result. For a successor cardinal κ, even assuming that κ<κ = κ and 2κ = κ+, the following is not provable in Zermelo–Fraenkel set theory. There is a κ+‐cc poset which does not collapse κ and which forces a(κ) = κ+ < ae(κ) = κ++ = 2κ. We also apply the ideas from the proofs of these results to study a = a(ω) and non(M). 2000 Mathematics Subject Classification 03E17 (primary), 03E05 (secondary).

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Feb 1, 2006

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