Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$0^{\sharp}$ and elementary end extensions of $V_{\kappa}$


Author: Amir Leshem
Journal: Proc. Amer. Math. Soc. 129 (2001), 2445-2450
MSC (1991): Primary 03E45, 03E55
Published electronically: January 18, 2001
MathSciNet review: 1823930
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract:

In this paper we prove that if $\kappa$ is a cardinal in $L[0^{\sharp}]$, then there is an inner model $M$ such that $M \models (V_{\kappa},\in)$ has no elementary end extension. In particular if $0^{\sharp}$ exists, then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than $\aleph_1$ of uncountable cofinality in $L[0^{\sharp}]$ is Mahlo in every strict inner model of $L[0^{\sharp}]$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E45, 03E55

Retrieve articles in all journals with MSC (1991): 03E45, 03E55


Additional Information

Amir Leshem
Affiliation: Institute of Mathematics, Hebrew University, Jerusalem, Israel
Address at time of publication: Circuit and Systems, Faculty of Information Technology and Systems, Mekelweg 4, 2628CD Delft, The Netherlands
Email: leshem@cas.et.tudelft.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05847-6
PII: S 0002-9939(01)05847-6
Keywords: Models of set theory, $0^{\sharp}$, inner models
Received by editor(s): October 19, 1999
Received by editor(s) in revised form: December 27, 1999
Published electronically: January 18, 2001
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2001 American Mathematical Society