Characterization of \mathcal L¹_κ

2023/03/19 by Siiri Kivimäki, Kivimaki, Siiri, Boban Veličković +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Mathematical and Theoretical Analysis #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2303.10759

Abstract

The logic \mathcal L¹_κ was introduced by Shelah in [3]. In [4], he proved that for a strongly compact cardinal κ, it admits the following algebraic characterization: two structures are \mathcal L¹_κ-equivalent if and only if they have isomorphic iterated ultrapowers via κ-complete ultrafilters. We give a presentation of the logic \mathcal L¹_κ and a simplified and slightly modified proof of this result.

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