Some specially formulated axiomizations for IΣ0 manage to evade the Herbrandized version of the Second Incompleteness Theorem

In 1981, Paris and Wilkie indicated it was an open question whether IΣ0 would satisfy the Second Incompleteness Theorem for Herbrand deduction. We will show that some specially formulated axiomizations for IΣ0 can evade the Herbrandized version of the Second Incompleteness Theorem.