Many countable support iterations of proper forcings preserve Souslin trees

Heike Mildenberger; Saharon Shelah

doi:10.1016/j.apal.2013.08.002

Many countable support iterations of proper forcings preserve Souslin trees

Heike Mildenberger^*, Saharon Shelah

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	573-608
Number of pages	36
Journal	Annals of Pure and Applied Logic
Volume	165
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2013.08.002
State	Published - Feb 2014
Externally published	Yes

Keywords

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

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10.1016/j.apal.2013.08.002

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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.",

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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

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JO - Annals of Pure and Applied Logic

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ER -

Many countable support iterations of proper forcings preserve Souslin trees

Abstract

Keywords

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