Elementary equivalence in positive logic via prime products

2023/03/05 by Moraschini, T., Wannenburg, J. J., Yamamoto, K. · 1 citation
#03C07 #03C10 #03C20 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2303.02614

Abstract

We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś's Theorem restricted to positive formulas, as well as the following variant of Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

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