ELEMENTARY EQUIVALENCE in POSITIVE LOGIC VIA PRIME PRODUCTS
Journal of Symbolic Logic, Year 2023
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We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Los's Theorem restricted to positive formulas, as well as the following variant of the 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.