Abstract
I define a homogeneous \(\aleph _2\)–c.c. proper product forcing for adding many clubs of \(\omega _1\) with finite conditions. I use this forcing to build models of \(\mathfrak {b}(\omega _1)=\aleph _2\), together with \(\mathfrak {d}(\omega _1)\) and \(2^{\aleph _0}\) large and with very strong failures of club guessing at \(\omega _1\).
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Asperó, D. Adding many Baumgartner clubs. Arch. Math. Logic 56, 797–810 (2017). https://doi.org/10.1007/s00153-017-0539-6
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DOI: https://doi.org/10.1007/s00153-017-0539-6
Keywords
- Baumgartner clubs
- Strong failures of club guessing
- Cardinal characteristics for \(\omega _1\)
- Generalizations of Martin’s Axiom