On certain lattices of degrees of interpretability.
Per Lindström · Notre Dame Journal of Formal Logic · 1984
PreliminariesAll theories S, T, A, B, etc., considered in what follows are primitive recursive (Craig's theorem).A, B, etc., are reflexive extensions of Peano arithmetic P. We write S \~ X or X H S, where X is a set of sentences, to mean that S h φ for every φ e X.Thus S H T means that S is a subtheory of T. S is an X-subtheory of T, S ~\χ Γ, if S h φ implies T h φ for every φ e X. S