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Polytime, combinatory logic and positive safe induction

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Abstract.

 We characterize the polynomial time operations as those which are provably total in a first order system, which comprises (untyped) combinatory logic with extensionality, together with positive “safe induction” on the set of binary strings. The formalization of safe induction is inspired by Leivants idea of ramification. We also show how to replace ramification by means of modal logic.

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  1. Dipartimento di Filosofia, Università di Firenze, via Bolognese 52, I-50139 Firenze, Italy. e-mail: cantini@philos.unifi.it, , , , , , IT

    Andrea Cantini

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  1. Andrea Cantini
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Received: 14 June 2000 / Published online: 20 December 2001

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Cantini, A. Polytime, combinatory logic and positive safe induction. Arch. Math. Logic 41, 169–189 (2002). https://doi.org/10.1007/s001530100105

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  • DOI: https://doi.org/10.1007/s001530100105

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