TY - JOUR
T1 - Many countable support iterations of proper forcings preserve Souslin trees
AU - Mildenberger, Heike
AU - Shelah, Saharon
PY - 2014/2
Y1 - 2014/2
N2 - 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 not.
AB - 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 not.
KW - Creature forcing
KW - Games played on forcing orders
KW - Non-elementary proper forcing
KW - Preservation theorems for trees on א
UR - http://www.scopus.com/inward/record.url?scp=84888000255&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2013.08.002
DO - 10.1016/j.apal.2013.08.002
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AN - SCOPUS:84888000255
SN - 0168-0072
VL - 165
SP - 573
EP - 608
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 2
ER -