The joint embedding property in normal open induction

AbstractThe models of normal open induction are those discretely ordered rings, integrally closed in their fraction field whose nonnegative part satisfy Peano's induction axioms for open formulas in the language of ordered semirings.It is known that neither open induction nor the usually studied stronger fragments of arithmetic (where induction for quantified formulas is allowed), have the joint embedding property.We prove that normal models of open induction have the joint embedding property