Elementary Cuts in Saturated Models of Peano Arithmetic

A model M = (M, +, X, 0, 1, <) of Peano Arithmetic (PA) is boundedly saturated if and only if it has a saturated elementary end extension N. The ordertypes of boundedly saturated models of PA are characterized and the number of models having these ordertypes is determined. Pairs (N, M), where,M <(end) N satisfies PA for saturated N, and their theories tire investigated. One result is: If N is a kappa-saturated model of PA and M-0, M-1 <(end) N are such that aleph(1) <= min(cf(M-0), dcf(M-0)) <= min(cf(M-1), dcf(M-1)) < kappa, then (N, M-0) equivalent to (N, M-1).