Comparing the degrees of enumerability and the closed Medvedev degrees

Medvedev Degrees, Muchnik Degrees, Subsystems of Z2 and Reverse Mathematics

Characterizing the Join-Irreducible Medvedev Degrees

We characterize the join-irreducible Medvedev degrees as the degrees of complements of Turing ideals, thereby solving a problem posed by Sorbi. 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 second-least degree. This solves a problem posed by Sorbi and Terwijn. Finally, we prove that t...

Kripke Models, Distributive Lattices, and Medvedev Degrees

We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice.

On relative enumerability of Turing degrees

Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in [ta] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least element m>0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that...

Non-branching degrees in the Medvedev lattice of Π01 classes

Special thanks to my advisor Steffen Lempp for his guidance and conversation. Abstract Always Sometimes 2 In this talk I will present the necessary background and then describe and characterize the non-branching degrees. Significantly, I will show three distinct classes of non-branching degrees. The Medvedev lattice of Π 0 1 classes is a lattice of certain subsets of 2 ω under a natural reducti...