Andrew Arana
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556
Andrew.Arana.1@nd.edu

Title: Degrees of n-diagrams of nonstandard models of arithmetic

Abstract: For a nonstandard model A of of first order Peano arithmetic
(PA), let SS(A) denote the Scott set (or standard system). Let D_n(A)
denote the n-diagram.  First, considering models of true arithmetic (TA),
we show that for any Scott set S which includes the arithmetical sets, the
following are the same for all n >= 1 :  {deg (D_n(A)) : A a nonstandard
model of TA with SS(A) = S}.
We then consider models of other completions of PA.

Reference

Knight, J.F.  "True Approximations and models of arithmetic", to appear in
Colloquium '97, ed. by Cooper and Truss