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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

REFERENCES

[1]Bekkali, M., Topics in set theory, Lecture Notes in Mathematics, vol. 1476 (1991).CrossRefGoogle Scholar
[2]Devlin, K., The Yorkshireman's guide to proper forcing, Surveys in set theory, London Mathematical Soceity Lecture Note Series, vol. 87, Cambridge University Press, 1983.Google Scholar
[3]Donder, H. and Fuchs, U., Handbook of set theory, To appear.Google Scholar
[4]Kunen, K., Set theory, an introduction to independense proofs, Studies in logic and the foundations of mathematics, vol. 102, North-Holland, 1980.Google Scholar
[5]Miyamoto, T., ω1-Souslin trees under countable support iterations, Fundamenta Mathematicae, vol. 142 (1993), pp. 256–261.CrossRefGoogle Scholar
[6]Schlindwein, C., Simplified RCS iterations, Archive for Mathematical Logic, vol. 32 (1993), pp. 341–349.CrossRefGoogle Scholar
[7]Shelah, S., Proper forcing, Lecture notes in mathematics, vol. 940, Springer-Verlag, 1982.Google Scholar
[8]Shelah, S., Iterated forcing and normal ideals on ω1, Israel Journal of Mathematics, vol. 60 (1987), pp. 345–380.CrossRefGoogle Scholar
[9]Shelah, S., Proper and improper forcing, Perspectives in mathematical logic, Springer, 1998.Google Scholar