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On iterating semiproper preorders

Published online by Cambridge University Press:  12 March 2014

Tadatoshi Miyamoto
Tadatoshi Miyamoto*
Affiliation:
Mathematics, Nanzan University, 18, Yamazato-Cho, Showa-Ku, Nagoya 4668673, Japan, E-mail: miyamoto@nanzan-u.ac.jp
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Abstract

Let T be an ω1-Souslin tree. We show the property of forcing notions; “is {ω1}-semi-proper and preserves T” is preserved by a new kind of revised countable support iteration of arbitrary length. As an application we have a forcing axiom which is compatible with the existence of an ω1 -Souslin tree for preorders as wide as possible.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1431 - 1468
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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