The isomorphism theorem for linear fragments of continuous logic

Seyed-Mohammad Bagheri

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arXiv · 1910.00776

The isomorphism theorem for linear fragments of continuous logic

Seyed-Mohammad Bagheri

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Abstract

The ultraproduct construction is generalized to $p$-ultramean constructions ($1\leqslant p<\infty$) by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments $\mathscr L^p$ of continuous logic. A powermean variant of Keisler-Shelah isomorphism theorem is proved for $\mathscr L^p$. It is then proved that $\mathscr L^p$-sentences (and their approximations) are exactly those sentences of continuous logic which are preserved by such constructions. Some other applications are also given.

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Seyed-Mohammad Bagheri. 2019-10-02. The isomorphism theorem for linear fragments of continuous logic. https://arxiv.org/abs/1910.00776

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