Enumerations and Computing Generics
Quasiminimal enumeration degrees and the computational strength of the total degrees above them, and the generic sets they compute.
SEMINARS & PRESENTATIONS
Invited talks.
Ahmad pairs and the local structure of the enumeration degrees
Characterizations of the left halves of Ahmad pairs and the separation between left and right halves in the local enumeration degrees.
Defining low₃, high₂ in the Σ₂ e-degrees
Using Ahmad pairs to obtain definitions of the low₃ and high₂ degrees in the language of the ordering of the Σ₂ enumeration degrees.
Enumeration Degrees — Local and Global Structure
A survey of enumeration reducibility and its relationship to Turing reducibility, contrasting the local structures of the enumeration and Turing degrees, followed by new work and open questions.
Contrasting the Halves of an Ahmad Pair
Ahmad pairs in the Σ⁰₂ enumeration degrees and their role as an obstacle to understanding the ∀∃ theory of the local structure.
Separating the Halves of an Ahmad Pair
Characterizing left halves of Ahmad pairs as low₃ and join-irreducible sets, and showing that right halves cannot be low₃.
Characterizing Ahmad Pairs in the Local Structure
A characterization of the left halves of Ahmad pairs, and a hierarchy of Ahmad n-pairs described through notions of join irreducibility.