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Cardinal Invariants and Eventually Different Functions
Author(s) -
Hyttinen Tapani
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930501831x
Subject(s) - successor cardinal , mathematics , corollary , mathematical proof , disjoint sets , mathematics subject classification , invariant (physics) , discrete mathematics , set theory , combinatorics , pure mathematics , set (abstract data type) , mathematical analysis , geometry , computer science , mathematical physics , programming language
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 a e (κ), b(κ) and a certain cardinal invariant m d (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 2 κ = 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 + < a e (κ) = κ ++ = 2 κ . 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).