Characterization of $\mathcal L^1_\kappa$

Siiri Kivimaki; Boban Velickovic

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arXiv · 2303.10759

Characterization of $\mathcal L^1_\kappa$

Siiri Kivimaki·Boban Velickovic

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Abstract

The logic $\mathcal L^1_\kappa$ was introduced by Shelah in [3]. In [4], he proved that for a strongly compact cardinal $\kappa$, it admits the following algebraic characterization: two structures are $\mathcal L^1_\kappa$-equivalent if and only if they have isomorphic iterated ultrapowers via $\kappa$-complete ultrafilters. We give a presentation of the logic $\mathcal L^1_\kappa$ and a simplified and slightly modified proof of this result.

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Siiri Kivimaki, Boban Velickovic. 2023-03-19. Characterization of $\mathcal L^1_\kappa$. https://arxiv.org/abs/2303.10759

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