Titel
Towers, mad families, and unboundedness
Abstract
We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are B-Canjar for any countably directed unbounded family B of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that b = ω1 in every extension by the above forcing notions.
Stichwort
TowersMaximal almost disjoint familiesUnboundednessCanjar filtersForcing
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
Erschienen in
Titel
Archive for Mathematical Logic
Band
62
Ausgabe
5-6
ISSN
0933-5846
Erscheinungsdatum
2023
Seitenanfang
811
Seitenende
830
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2023
Zugänglichkeit
Rechte
Rechteangabe
© The Author(s) 2023, corrected publication 2023
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