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Model theoretic characterizations of large cardinals

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Abstract

We consider compactness characterizations of large cardinals. Based on results of Benda [Ben78], we study compactness for omitting types in various logics. In \(\mathbb{L}\)κ,κ, this allows us to characterize any large cardinal defined in terms of normal ultrafilters, and we also analyze second-order and sort logic. In particular, we give a compactness for omitting types characterization of huge cardinals, which have consistency strength beyond Vopĕnka’s Principle.

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Authors and Affiliations

  1. Department of Mathematics, Texas State University, San Marcos, TX, 7866, USA

    Will Boney

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  1. Will Boney
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Correspondence to Will Boney.

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This material is based upon work done while the author was supported by the National Science Foundation under Grant No. DMS-1402191.

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Boney, W. Model theoretic characterizations of large cardinals. Isr. J. Math. 236, 133–181 (2020). https://doi.org/10.1007/s11856-020-1971-6

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  • DOI: https://doi.org/10.1007/s11856-020-1971-6

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