Thomas F. Kent

s-degrees within e-degrees

For any enumeration degree a let Das be the set of s-degrees contained in a. We answer an open question of Watson by showing that if a is a nontrivial Σ20-enumeration degree, then Das has no least element. We also show that every countable partial order embeds into Das.

The structure of the s-degrees contained within a single e-degree

Abstract For any enumeration degree a let D a s be the set of s -degrees contained in a . We answer an open question of Watson by showing that if a is a nontrivial Σ 2 0 -enumeration degree, then D a s has no least element. We also show that every countable partial order embeds into D a s . Finally, we construct Σ 2 0 -sets A and B such that B ≤ e A but for every X ≡ e B , X ≰ s A .

A note on the enumeration degrees of 1-generic sets

We show that every nonzero

Image analysis and fractal geometry to characterize soil desiccation cracks

{\Delta^{0}_{2}}

Undecidability of local structures of s-degrees and Q-degrees

Δ20 enumeration degree bounds the enumeration degree of a 1-generic set. We also point out that the enumeration degrees of 1-generic sets, below the first jump, are not downwards closed, thus answering a question of Cooper.

Bounding Nonsplitting Enumeration Degrees

There is a π20 enumeration degree which is a strong minimal cover. This is the best result possible since the Σ20 enumeration degrees are dense. A priority proof using doubling requests is used to construct the required sets.