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

 

Souslin trees which are hard to specialise


Author: James Cummings
Journal: Proc. Amer. Math. Soc. 125 (1997), 2435-2441
MSC (1991): Primary 03E05; Secondary 03E35
MathSciNet review: 1376756
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Abstract: We construct some $\kappa ^+$-Souslin trees which cannot be specialised by any forcing which preserves cardinals and cofinalities. For $\kappa $ a regular cardinal we use the $ \begin {picture}(6,6)(0,0) \drawline (0,3)(3,6)(6,3) (3,0)(0,3) \drawline (0,6)(6,6)(6,0) (0,0)(0,6) \end {picture} $ principle, and for $\kappa $ singular we use squares and diamonds.


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Additional Information

James Cummings
Affiliation: Mathematics Institute, Hebrew University, Givat Ram, 91904 Jerusalem, Israel
Address at time of publication: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213-3890
Email: cummings@math.huji.ac.il, jcumming@andrew.cmu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03796-9
PII: S 0002-9939(97)03796-9
Keywords: Souslin trees, ascent paths, squares and diamonds
Received by editor(s): September 7, 1995
Received by editor(s) in revised form: February 12, 1996
Additional Notes: The author was supported by a Postdoctoral Fellowship at the Mathematics Institute, Hebrew University of Jerusalem
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society