David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 74 (3):1015-1046 (2009)
The motivation for this paper is the following: In  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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Gunter Fuchs (2010). Generic Embeddings Associated to an Indestructibly Weakly Compact Cardinal. Annals of Pure and Applied Logic 162 (1):89-105.
Similar books and articles
Joel David Hamkins (1999). Gap Forcing: Generalizing the Lévy-Solovay Theorem. Bulletin of Symbolic Logic 5 (2):264-272.
Jouko Väänänen (1982). Abstract Logic and Set Theory. II. Large Cardinals. Journal of Symbolic Logic 47 (2):335-346.
Gunter Fuchs (2008). Closed Maximality Principles: Implications, Separations and Combinations. Journal of Symbolic Logic 73 (1):276-308.
Andrés Villaveces (1998). Chains of End Elementary Extensions of Models of Set Theory. Journal of Symbolic Logic 63 (3):1116-1136.
Joel David Hamkins (2003). A Simple Maximality Principle. Journal of Symbolic Logic 68 (2):527-550.
Itay Neeman & Jindřich Zapletal (2001). Proper Forcing and L(ℝ). Journal of Symbolic Logic 66 (2):801-810.
Ralf-Dieter Schindler (2001). Proper Forcing and Remarkable Cardinals II. Journal of Symbolic Logic 66 (3):1481-1492.
Natasha Dobrinen & Sy-David Friedman (2006). Co-Stationarity of the Ground Model. Journal of Symbolic Logic 71 (3):1029 - 1043.
Stephen H. Hechler (2001). On Consistent Subsets of Large Sets of Satisfiable Sentences. Studia Logica 69 (3):339-349.
Theodore Sider (2001). Maximality and Intrinsic Properties. Philosophy and Phenomenological Research 63 (2):357 - 364.
Theodore Sider (2003). Maximality and Microphysical Supervenience. Philosophy and Phenomenological Research 66 (1):139-149.
Ralf-Dieter Schindler (1999). Successive Weakly Compact or Singular Cardinals. Journal of Symbolic Logic 64 (1):139-146.
Arthur W. Apter & Joel David Hamkins (2003). Exactly Controlling the Non-Supercompact Strongly Compact Cardinals. Journal of Symbolic Logic 68 (2):669-688.
Added to index2010-09-12
Total downloads5 ( #227,338 of 1,101,679 )
Recent downloads (6 months)2 ( #178,427 of 1,101,679 )
How can I increase my downloads?