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Families of sets whose pairwise intersections have prescribed cardinals or order types Corrigenda
Published online by Cambridge University Press: 24 October 2008
Extract
(i) J. Baumgartner has kindly drawn our attention to the fact that Theorem 2 as stated in (1) is false. A counter example is the case in which m = ℵ2; n = ℵ1; p = ℵ0. For by reference (3) of the paper (1) there is an almost disjoint family (Aγ: γ < ω1) of infinite subsets of ω̲ Put Aν = ω̲ for ω1 ≤ ν < ω2. Then, contrary to the assertion of that theorem, all conditions of Theorem 2 are satisfied. However, Theorem 2 becomes correct if the hypothesis
is strengthened to
In fact, Baumgartner has proved the desired conclusion under the weaker hypothesis
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 3 , May 1977 , pp. 523
- Copyright
- Copyright © Cambridge Philosophical Society 1977