Extendible sets in peano arithmetic

Let A be a structure and let U be a subset of \A\. We say U is extendible if whenever B is an elementary extension of A.there is a V ⊆B\ such that (A, U) < (B, V). Our main results are: If Jt is a countable model of Peano arithmetic and U is a subset of M, then U is extendible iff U is parametrically definable in M. Also, the cofinally extendible subsets of \M\ are exactly the inductive subsets of \M\. The end extendible subsets of \M\ are not completely characterized, but we show that if N is a model of Peano arithmetic of arbitrary cardinality and U is any bounded subset of jr", then U is end extendible.