Moraschini, TommasoWannenburg, Johann JoubertYamamoto, Kentaro2024-10-022024-10-022025-09Moraschini, T., Wannenburg, J. & Yamamoto, K. 2025, 'Elementary equivalence in positive logic via prime products', The Journal of Symbolic Logic, vol. 90, no. 3, pp. 1129-1146, doi:10.1017/jsl.2023.50.0022-4812 (print)1943-5886 (online)10.1017/jsl.2023.50http://hdl.handle.net/2263/98433We 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.en© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic.H-inductive theoryPositively existentially closed modelPrime productPositive model theoryKeisler isomorphism theoremPreprint Article