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The almost-disjointness number may have countable cofinality

Author: Jörg Brendle
Journal: Trans. Amer. Math. Soc. 355 (2003), 2633-2649
MSC (2000): Primary 03E17; Secondary 03E35
Published electronically: February 27, 2003
MathSciNet review: 1975392
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Abstract: We show that it is consistent for the almost-disjointness number $\mathfrak{a}$ to have countable cofinality. For example, it may be equal to $\aleph_\omega$.

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Additional Information

Jörg Brendle
Affiliation: The Graduate School of Science and Technology, Kobe University, Rokko–dai 1–1, Nada–ku, Kobe 657–8501, Japan

Keywords: Maximal almost-disjoint families, almost-disjointness number, iterated forcing.
Received by editor(s): October 3, 2001
Published electronically: February 27, 2003
Additional Notes: Supported by Grant–in–Aid for Scientific Research (C)(2)12640124, Japan Society for the Promotion of Science
Article copyright: © Copyright 2003 American Mathematical Society