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Provability Logics for Relative Interpretability

In: Mathematical Logic

Author

Listed:
  • Dick de Jongh

    (University of Amsterdam, Department of Mathematics and Computer Science)

  • Frank Veltman

    (University of Amsterdam, Department of Philosophy)

Abstract

In this paper the system IL for relative interpretability described in Visser (1988) is studied.1 In IL formulae A ⊳ B (read: A interprets B) are added to the provability logic L. The intended interpretation of a formula A ⊳ B in an (arithmetical) 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 (Švejdar 1983, Montagna 1984, Visser 1986, 1988P).

Suggested Citation

  • Dick de Jongh & Frank Veltman, 1990. "Provability Logics for Relative Interpretability," Springer Books, in: Petio Petrov Petkov (ed.), Mathematical Logic, pages 31-42, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0609-2_3
    DOI: 10.1007/978-1-4613-0609-2_3
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