The combinatorial essence of supercompactness

Annals of Pure and Applied Logic 163 (11):1710-1717 (2012)
  Copy   BIBTEX

Abstract

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal. Utilizing the failure of a weak version of a square, we show that the best currently known lower bounds for the consistency strength of these principles can be applied

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2011.12.017

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Inner models and ultrafilters in l(r).Itay Neeman - 2007 - Bulletin of Symbolic Logic 13 (1):31-53.
On measurable limits of compact cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
Indestructibility and the level-by-level agreement between strong compactness and supercompactness.Arthur W. Apter & Joel David Hamkins - 2002 - Journal of Symbolic Logic 67 (2):820-840.
A combinatorial forcing for coding the universe by a real when there are no sharps.Saharon Shelah & Lee J. Stanley - 1995 - Journal of Symbolic Logic 60 (1):1-35.
Some combinatorial and algorithmic problems in many-valued logics.Ivan Stojmenović - 1987 - Novi Sad: University of Novi Sad, Faculty of Science, Institute of Mathematics.
Duns Scotus on Singular Essences.Peter King - 2005 - Medioevo 30:111-137.
Pκλ combinatorics II: The RK ordering beneath a supercompact measure.William S. Zwicker - 1986 - Journal of Symbolic Logic 51 (3):604 - 616.
Incompatible extensions of combinatorial functions.Erik Ellentuck - 1983 - Journal of Symbolic Logic 48 (3):752-755.
The Epistemology of Essence.Tuomas Tahko - 2018 - In Alexander Carruth, S. C. Gibb & John Heil (eds.), Ontology, Modality, Mind: Themes from the Metaphysics of E. J. Lowe. Oxford, UK: Oxford University Press. pp. 93-110.
From neural dynamics to true combinatorial structures.Frank van der Velde & Marc de Kamps - 2006 - Behavioral and Brain Sciences 29 (1):88-104.
Topological Aspects of Combinatorial Possibility.Thomas Mormann - 1997 - Logic and Logical Philosophy 5:75 - 92.

Analytics

Added to PP
2013-10-27

Downloads
12 (#1,058,801)

6 months
2 (#1,232,442)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Small embedding characterizations for large cardinals.Peter Holy, Philipp Lücke & Ana Njegomir - 2019 - Annals of Pure and Applied Logic 170 (2):251-271.
A refinement of the Ramsey hierarchy via indescribability.Brent Cody - 2020 - Journal of Symbolic Logic 85 (2):773-808.
Guessing models and generalized Laver diamond.Matteo Viale - 2012 - Annals of Pure and Applied Logic 163 (11):1660-1678.
Quotients of strongly proper forcings and guessing models.Sean Cox & John Krueger - 2016 - Journal of Symbolic Logic 81 (1):264-283.

View all 15 citations / Add more citations

References found in this work

Stacking mice.Ronald Jensen, Ernest Schimmerling, Ralf Schindler & John Steel - 2009 - Journal of Symbolic Logic 74 (1):315-335.
A general Mitchell style iteration.John Krueger - 2008 - Mathematical Logic Quarterly 54 (6):641-651.
Forcing Indestructibility of Set-Theoretic Axioms.Bernhard König - 2007 - Journal of Symbolic Logic 72 (1):349 - 360.

Add more references