An isomorphism theorem for models of Weak König's Lemma without primitive recursion

Abstract

We prove that if (M, X ) and (M, Y) are countable models of the theory WKL * 0 such that IΣ1(A) fails for some A ∈ X ∩Y, then (M, X ) and (M, Y) are isomorphic. As a consequence, the analytic hierarchy collapses to ∆ 1