Many countable support iterations of proper forcings preserve Souslin trees

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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 not.

MSC

03E05
03E17
03E35
03E15

Keywords

Games played on forcing orders
Creature forcing
Non-elementary proper forcing
Preservation theorems for trees on 1

Cited by (0)

The first author acknowledges Marie Curie grant PIEF-2008-219292 of the European Union. The second authorʼs research was partially supported by the United States–Israel Binational Science Foundation (Grant no. 2002323). This is the second authorʼs publication no. 973.