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2014 Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence
Arthur W. Apter
Notre Dame J. Formal Logic 55(4): 431-444 (2014). DOI: 10.1215/00294527-2798691

Abstract

We construct models for the level-by-level equivalence between strong compactness and supercompactness containing failures of the Generalized Continuum Hypothesis (GCH) at inaccessible cardinals. In one of these models, no cardinal is supercompact up to an inaccessible cardinal, and for every inaccessible cardinal δ, 2δ>δ++. In another of these models, no cardinal is supercompact up to an inaccessible cardinal, and the only inaccessible cardinals at which GCH holds are also measurable. These results extend and generalize earlier work of the author.

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Arthur W. Apter. "Inaccessible Cardinals, Failures of GCH, and Level-by-Level Equivalence." Notre Dame J. Formal Logic 55 (4) 431 - 444, 2014. https://doi.org/10.1215/00294527-2798691

Information

Published: 2014
First available in Project Euclid: 7 November 2014

zbMATH: 1335.03044
MathSciNet: MR3276406
Digital Object Identifier: 10.1215/00294527-2798691

Subjects:
Primary: 03E35, 03E55

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 4 • 2014
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