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Many countable support iterations of proper forcings preserve Souslin trees
Annals of Pure and Applied Logic 165 (2):573-608 (2014)
Abstract
We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation properties in countable support iterations in the so-called Case A that does not need a division into forcings that add reals and those who do notMy notes
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References found in this work
There may be simple Pℵ1 and Pℵ2-points and the Rudin-Keisler ordering may be downward directed.Andreas Blass & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (C):213-243.
Near coherence of filters. III. A simplified consistency proof.Andreas Blass & Saharon Shelah - 1989 - Notre Dame Journal of Formal Logic 30 (4):530-538.
Reasonable Ultrafilters, Again.Andrzej Rosłanowski & Saharon Shelah - 2011 - Notre Dame Journal of Formal Logic 52 (2):113-147.
Cardinal invariants of the continuum and combinatorics on uncountable cardinals.Jörg Brendle - 2006 - Annals of Pure and Applied Logic 144 (1-3):43-72.
New reals: Can live with them, can live without them.Martin Goldstern & Jakob Kellner - 2006 - Mathematical Logic Quarterly 52 (2):115-124.
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