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- Self-referential theories.Samuel A. Alexander - 2020 - Journal of Symbolic Logic 85 (4):1687-1716.We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.
- Advances in Modal Logic, Vol. 13.Nicola Olivetti & Rineke Verbrugge (eds.) - 2020 - College Publications.
- On the provability logic of bounded arithmetic.Rineke Verbrugge & Alessandro Berarducci - 1991 - Annals of Pure and Applied Logic 61 (1-2):75-93.Let PLω be the provability logic of IΔ0 + ω1. We prove some containments of the form L ⊆ PLω < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke frames.
- Provability logics for relative interpretability.Frank Veltman & Dick De Jongh - 1990 - In Petio Petrov Petkov (ed.), Mathematical Logic. Proceedings of the Heyting '88 Summer School. New York, NY, USA: pp. 31-42.In this paper the system IL for relative interpretability is studied.
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