No CrossRef data available.
Article contents
PRESERVATION OF SUSLIN TREES AND SIDE CONDITIONS
Published online by Cambridge University Press: 29 June 2016
Abstract
We show how to force, with finite conditions, the forcing axiom PFA(T), a relativization of PFA to proper forcing notions preserving a given Suslin tree T. The proof uses a Neeman style iteration with generalized side conditions consisting of models of two types, and a preservation theorem for such iterations. The consistency of this axiom was previously known using a standard countable support iteration and a preservation theorem due to Miyamoto.
- Type
- Articles
- Information
- Copyright
- Copyright © The Association for Symbolic Logic 2016
References
REFERENCES
Miyamoto, Tadoshi,
ω
1-Suslin trees under countable support iterations. Fundamenta Mathematicae, vol. 143 (1993), pp. 257–261.Google Scholar
Neeman, Itay,
Forcing with sequences of models of two types
. Notre Dame Journals of Formal Logic, vol. 55 (2014), pp. 265–298.Google Scholar
Todorčević, Stevo, Forcing with a coherent Suslin tree, preprint.Google Scholar
Veličković, Boban and Venturi, Giorgio,
Proper forcing remastered
, Appalachian Set Theory (Cummings, Schimmerling, editors), LMS lecture notes series, vol. 46 (2012), pp. 231–261.Google Scholar