The amalgamation property in normal open induction.
Margarita Otero · Notre Dame Journal of Formal Logic · 1992
It is known that open induction (OI), the fragment of Peano arithmetic, fails to have the joint embedding property, a result due to Wilkie.On the other hand we have proved that if we require our models to be normal, that is, to be integrally closed in their fraction fields, the corresponding theory NOI extending OI, has the joint embedding property.Here we prove NOI does not have the amalgamation property.