On cofinal submodels and elementary interstices (Q1762352)

The paper is devoted to the study of structures of the form \((N,M)\) where \(N\) is a countable recursively saturated model of Peano arithmetic PA and \(M\) is its cofinal submodel. A number of results concerning the variety of first-order theories and isomorphism types of pairs of this form are proved. Two new isomorphism invariants for such pairs are identified. Continuum many theories of such pairs with the fixed greatest common initial segment of \(N\) and \(M\) and fixed lattice of interstructures \(K\) such that \(M \prec K \prec N\) are obtained.