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2013 The Nonabsoluteness of Model Existence in Uncountable Cardinals for Lω1,ω
Sy-David Friedman, Tapani Hyttinen, Martin Koerwien
Notre Dame J. Formal Logic 54(2): 137-151 (2013). DOI: 10.1215/00294527-1960443

Abstract

For sentences ϕ of Lω1,ω, we investigate the question of absoluteness of ϕ having models in uncountable cardinalities. We first observe that having a model in 1 is an absolute property, but having a model in 2 is not as it may depend on the validity of the continuum hypothesis. We then consider the generalized continuum hypothesis (GCH) context and provide sentences for any αω1{0,1,ω} for which the existence of a model in α is nonabsolute (relative to large cardinal hypotheses). Finally, we present a complete sentence for which model existence in 3 is nonabsolute.

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Sy-David Friedman. Tapani Hyttinen. Martin Koerwien. "The Nonabsoluteness of Model Existence in Uncountable Cardinals for Lω1,ω." Notre Dame J. Formal Logic 54 (2) 137 - 151, 2013. https://doi.org/10.1215/00294527-1960443

Information

Published: 2013
First available in Project Euclid: 21 February 2013

zbMATH: 1285.03045
MathSciNet: MR3028792
Digital Object Identifier: 10.1215/00294527-1960443

Subjects:
Primary: 03C48
Secondary: 03C75

Rights: Copyright © 2013 University of Notre Dame

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Vol.54 • No. 2 • 2013
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