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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Morasses and finite support iterations


Author: Bernhard Irrgang
Journal: Proc. Amer. Math. Soc. 137 (2009), 1103-1113
MSC (2000): Primary 03E05, 03E35, 03E40
Published electronically: August 28, 2008
MathSciNet review: 2457452
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Abstract: We introduce a method of constructing a forcing along a simplified $ (\kappa,1)$-morass such that the forcing satisfies the $ \kappa$-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain condition. As an application, we construct a ccc forcing that adds an $ \omega_2$-Suslin tree. Related methods are Shelah's historic forcing and Todorcevic's $ \rho$-functions.


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Additional Information

Bernhard Irrgang
Affiliation: Mathematisches Institut, Universität Bonn, Beringstrasse 1, 53115 Bonn, Germany

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09525-7
PII: S 0002-9939(08)09525-7
Received by editor(s): October 6, 2006
Received by editor(s) in revised form: April 22, 2007, and February 1, 2008
Published electronically: August 28, 2008
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.