Journal of Symbolic Logic

Combined Maximality Principles up to large cardinals

Gunter Fuchs

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The motivation for this paper is the following: In [4] I showed that it is inconsistent with ZFC that the Maximality Principle for directed closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the Maximality Principle for < κ-closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regular cardinals or at every regular cardinal below some large cardinal κ (instead of ∞), and if so, how strong it is. It turns out that it is consistent in many cases, but the consistency strength is quite high.

Article information

J. Symbolic Logic, Volume 74, Issue 3 (2009), 1015-1046.

First available in Project Euclid: 16 June 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Fuchs, Gunter. Combined Maximality Principles up to large cardinals. J. Symbolic Logic 74 (2009), no. 3, 1015--1046. doi:10.2178/jsl/1245158097.

Export citation