Abstract
It is known that full Peano Arithmetic does not have the joint embedding property(JEP). At the other extreme of the hierarchy, Open Induction also fails to have this property. We prove, using some conservation results about fragments of arithmetic, that if T is a theoryconsistent with PA and T ⊢ I E 1 − (bounded existential parameter-free induction), then any two m dels of PA which jointly embed in a model of T also jointly embed in an elementary extension of one of them. In particular, any fragment of PA extending I E 1 − fails to have JEP.
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