4 NATURAL FACTORS OF THE MEDVEDEV LATTICE CAPTURING IPC
Rutger Kuyper · 2016
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 $${ eg p \vee eg eg p}$$ . This answers a question by Sorbi and Terwijn.