On well-splitting posets

DOI10.1007/S00153-022-00818-6arXiv2204.08257MaRDI QIDQ6396762

Dušan Repovš, Lyubomyr Zdomskyy

Publication date: 18 April 2022

Abstract: We introduce a class of proper posets which is preserved under countable support iterations, includes $omeg{a}^{o}mega$-bounding, Cohen, Miller, and Mathias posets associated to filters with the Hurewicz covering properties, and has the property that the ground model reals remain splitting and unbounded in corresponding extensions. Our results may be considered as a possible path towards solving variations of the famous Roitman problem.

Mathematics Subject Classification ID

Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Consistency and independence results (03E35) Cardinal characteristics of the continuum (03E17)

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