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PRESERVATION OF SUSLIN TREES AND SIDE CONDITIONS

Published online by Cambridge University Press:  29 June 2016

GIORGIO VENTURI
GIORGIO VENTURI*
Affiliation:
CENTRO DE LÓGICA EPISTEMOLOGIA E HISTÓRIA DE LA CIÊNCIA UNIV. EST. DE CAMPINAS. RUA SÉRGIO BUARQUE DE HOLANDA 251 BARÃO GERALDO, SP., BRAZILE-mail:[email protected]
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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.

Keywords

03E3503E6503E57forcingproperside conditionsSuslin treePFA
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016 , pp. 483 - 492
Copyright
Copyright © The Association for Symbolic Logic 2016 

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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