10 research outputs found
Natural Factors of the Medvedev Lattice Capturing IPC
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
Intuitionistic logic and Muchnik degrees
We prove that there is a factor of the Muchnik lattice that captures intuitionistic propositional logic. This complements a now classic result of Skvortsova for the Medvedev lattice
The degree structure of Weihrauch-reducibility
We answer a question by Vasco Brattka and Guido Gherardi by proving that the
Weihrauch-lattice is not a Brouwer algebra. The computable Weihrauch-lattice is
also not a Heyting algebra, but the continuous Weihrauch-lattice is. We further
investigate the existence of infinite infima and suprema, as well as embeddings
of the Medvedev-degrees into the Weihrauch-degrees
Intermediate logics and factors of the Medvedev lattice
AbstractWe investigate the initial segments of the Medvedev lattice as Brouwer algebras, and study the propositional logics connected to them