On well-splitting posets

On well-splitting posets

We introduce a class of proper posets which is preserved under countable support iterations, includes ω ω -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 corre...

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Veröffentlicht in:Archive for mathematical logic 2022-11, Vol.61 (7-8), p.995-1005
Hauptverfasser: Repovš, Dušan, Zdomskyy, Lyubomyr
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Sprache:eng
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Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Set theory
Splitting
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Zdomskyy, Lyubomyr
description We introduce a class of proper posets which is preserved under countable support iterations, includes ω ω -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.
doi_str_mv 10.1007/s00153-022-00818-6
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subjects Algebra
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Set theory
Splitting
title On well-splitting posets
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