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).
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Bibliography
F. Montagna, 1984, Provability in finite subtheories of PA and Relative Interpretability: a Modal Investigation, Rapporto Matematico 118, Dipartimento di Matematica, Universita di Siena.
V. Švejdar, 1983, Modal Analysis of generalized Rosser sentences, Journal of Symbolic Logic 48, p. 986–999.
C. Smoryński, 1985, Modal Logic and Self-reference, Springer-Verlag, New York
A. Visser, 1986, Peano’s Smart Children, a provability-logical study of systems with built-in consistency, Logic Group Preprint Series No. 14, Department of Philosophy, University of Utrecht, to be published in The Notre Dame Journal of Formal Logic.
A. Visser, 1988P, Preliminary Notes on Interpretability Logic, Logic Group Preprint Series No. 29, Department of Philosophy, University of Utrecht.
A. Visser, 1988, Interpretability Logic, This Volume.
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© 1990 Plenum Press, New York
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de Jongh, D., Veltman, F. (1990). Provability Logics for Relative Interpretability. In: Petkov, P.P. (eds) Mathematical Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0609-2_3
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DOI: https://doi.org/10.1007/978-1-4613-0609-2_3
Publisher Name: Springer, Boston, MA
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