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ON FOREMAN’S MAXIMALITY PRINCIPLE

Published online by Cambridge University Press:  29 September 2016

MOHAMMAD GOLSHANI  and
YAIR HAYUT
MOHAMMAD GOLSHANI
Affiliation:
SCHOOL OF MATHEMATICS INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM) P.O. BOX: 19395-5746, TEHRAN, IRANE-mail: [email protected]
YAIR HAYUT
Affiliation:
THE HEBREW UNIVERSITY OF JERUSALEM EINSTEIN INSTITUTE OF MATHEMATICS EDMOND J. SAFRA CAMPUS, GIVAT RAM JERUSALEM 91904, ISRAELE-mail: [email protected]
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Abstract

In this paper, we consider Foreman’s maximality principle, which says that any nontrivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We observe that it is consistent that every c.c.c. forcing adds a real and that for every uncountable regular cardinal κ, every κ-closed forcing of size 2<κ collapses some cardinal.

Keywords

adding realscollapsing cardinalsextender sequencesextender based Radin forcing
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 4 , December 2016 , pp. 1344 - 1356
Copyright
Copyright © The Association for Symbolic Logic 2016 

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