Natural Factors of the Medvedev Lattice Capturing IPC
Logic
2015-07-14 v2
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 for every non-trivial factor of the Medvedev lattice its theory is contained in Jankov's logic, the deductive closure of IPC plus the weak law of the excluded middle. This answers a question by Sorbi and Terwijn.
Keywords
Cite
@article{arxiv.1311.2010,
title = {Natural Factors of the Medvedev Lattice Capturing IPC},
author = {Rutger Kuyper},
journal= {arXiv preprint arXiv:1311.2010},
year = {2015}
}