Provability Logics for Relative Interpretability

In this paper the system IL for relative interpretability described in Visser is studied.1 In IL formulae A|> B are added to the provability logic L. The intended interpretation of a formula A|> B in an theory T is: T + B is relatively interpretable in T + A. The system has been shown to be sound with respect to such arithmetical interpretations. As axioms for IL we take the usual axioms A→ A and → A for the provability logic L and its rules, modus ponens and necessitation, plus the axioms: → ∧ → ∧ → → A|>A With respect to priority of parentheses |> is treated as →
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