We introduce prime products as a generalization of ultraproducts for positive
logic. Prime products are shown to satisfy a version of {\L}o\'s'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.Comment: 15 page