$0^{\sharp }$ and elementary end extensions of $V_{\kappa }$
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- by Amir Leshem PDF
- Proc. Amer. Math. Soc. 129 (2001), 2445-2450 Request permission
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
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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
- 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.
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2445-2450
- MSC (1991): Primary 03E45, 03E55
- DOI: https://doi.org/10.1090/S0002-9939-01-05847-6
- MathSciNet review: 1823930