Natural factors of the Medvedev lattice capturing IPC |
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Authors: | Rutger Kuyper |
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Affiliation: | 1. Department of Mathematics, Radboud University Nijmegen, P.O. Box 9010, 6500 GL, Nijmegen, The Netherlands
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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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