On cofinal extensions of models of fragments of arithmetic.
Richard W. Kaye · Notre Dame Journal of Formal Logic · 1991
We present a model-theoretic proof of Motohashi's preservation theorem for cofinal extensions, and examine various criteria for a model of a fragment of PA to have a proper elementary cofinal extension.Using these criteria we answer a question of Roman Kossak's, exhibiting for each n > 0 countable models M and TV of IΣ n + exp + -ι2?Σ Λ+1 such that: (i) M has no proper elementary cofinal extensions and (ii) N does have proper elementary cofinal extensions.