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Natural factors of the Medvedev lattice capturing IPC

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Abstract

Skvortsova showed that there is a factor of the Medvedev lattice which captures intuitionistic propositional logic (IPC). However, her factor is unnatural in the sense that it is constructed in an ad hoc manner. We present a more natural example of such a factor. We also show that the theory of every non-trivial factor of the Medvedev lattice is contained in Jankov’s logic, the deductive closure of IPC plus the weak law of the excluded middle \({\neg p \vee \neg \neg p}\). This answers a question by Sorbi and Terwijn.

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Authors and Affiliations

  1. Department of Mathematics, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands

    Rutger Kuyper

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  1. Rutger Kuyper
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Correspondence to Rutger Kuyper.

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Research supported by NWO/DIAMANT grant 613.009.011 and by John Templeton Foundation grant 15619: ‘Mind, Mechanism and Mathematics: Turing Centenary Research Project’.

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Kuyper, R. Natural factors of the Medvedev lattice capturing IPC. Arch. Math. Logic 53, 865–879 (2014). https://doi.org/10.1007/s00153-014-0393-8

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