We use this characterization to prove that there are Medvedev degrees above the second-least degree that do not bound any join-irreducible degrees above this ...

We characterize the join-irreducible Medvedev degrees as the degrees of complements of Turing ideals, thereby solving a problem posed by Sorbi.

We characterize the join-irreducible Medvedev degrees as the degrees of complements of Turing ideals, thereby solving a problem posed by Sorbi.

We characterize the join-irreducible Medvedev degrees and deduce several consequences for the in- terpretation of propositional logic in the Medvedev degrees.

Problem 5.4 Characterize the join-irreducible elements. Page 12. 300. Andrea Sorbi. 6 More on the degrees of enumerability. The. Dyment lattice. In this section ...

Paul Shafer, “Characterizing the Join-Irreducible Medvedev Degrees”, Notre Dame J. Formal Logic, 52:1 (2011) crossref.

... degrees are dense, Annals of Mathematics 80 (1964) 300–312. [31] P. Shafer, Characterizing the join-irreducible Medvedev degrees, Notre Dame Journal of ...

An element D is join-reducible if there are A and B incomparable such that A + B = D. Note that M satisfies ¬A ∨ ¬¬A because 1 is join-irreducible: Proposition ...

Our coding methods also prove that neither the closed Medvedev degrees nor the compact Medvedev degrees are elementarily equivalent to either the closed Muchnik ...

This paper investigates some filters and ideals of the Medvedev lattice of M, finding some of them already introduced by Dyment, [4], and investigates the ...