On Foreman’s maximality principle

Mohammad Golshani; Yair Hayut

doi:10.1017/jsl.2016.21

On Foreman’s maximality principle

Mohammad Golshani
, Yair Hayut

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	1344-1356
Number of pages	13
Journal	Journal of Symbolic Logic
Volume	81
Issue number	4
DOIs	https://doi.org/10.1017/jsl.2016.21
State	Published - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2016, Association for Symbolic Logic.

Keywords

Adding reals
Collapsing cardinals
Extender based Radin forcing
Extender sequences

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10.1017/jsl.2016.21

Cite this

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On Foreman’s maximality principle

Abstract

Bibliographical note

Keywords

Access to Document

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