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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Maharam algebras and Cohen reals


Authors: Ilijas Farah and Boban Velickovic
Journal: Proc. Amer. Math. Soc. 135 (2007), 2283-2290
MSC (2000): Primary 03Exx; Secondary 28Axx
Published electronically: February 2, 2007
MathSciNet review: 2299506
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Abstract: We show that the product of any two nonatomic Maharam algebras adds a Cohen real. As a corollary of this and a result of Shelah (1994) we obtain that the product of any two nonatomic ccc Souslin forcing notions adds a Cohen real.


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Additional Information

Ilijas Farah
Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
Address at time of publication: Matematički Institut, Kneza Mihaila 35, Beograd, Serbia and Montenegro
Email: ifarah@mathstat.yorku.ca

Boban Velickovic
Affiliation: Equipe de Logique Mathématique, UFR de Mathématiques (case 7012), Université Denis-Diderot Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France
Address at time of publication: Matematički Institut, Kneza Mihaila 35, Beograd, Serbia and Montenegro
Email: boban@logique.jussieu.fr

DOI: https://doi.org/10.1090/S0002-9939-07-08759-X
Keywords: Exhaustive submeasure, Maharam algebra, Cohen real
Received by editor(s): March 8, 2006
Published electronically: February 2, 2007
Additional Notes: These results were obtained in December 2004 while the authors were visiting the E. Schrödinger Institute in Vienna. We would like to thank the Institute for providing hospitality and a stimulating environment. The first author was partially supported by NSERC
Communicated by: Julia Knight
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.