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ELEMENTARY EQUIVALENCE IN POSITIVE LOGIC VIA PRIME PRODUCTS
Published online by Cambridge University Press: 05 July 2023
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 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.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic