APAL
2011
13 years 5 months ago
2011
We define a new NP search problem, the “local improvement” principle, about labellings of an acyclic, bounded-degree graph. We show that, provably in PV, it characterizes the...
APAL
2011
13 years 5 months ago
2011
The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are indepe...
APAL
2011
13 years 5 months ago
2011
We develop the theory of domination by stable types and stable weight in an arbitrary theory.
APAL
2011
13 years 5 months ago
2011
Abstract. We give classical proofs, strengthenings, and generalizations of Lecomte’s characterizations of analytic ω-dimensional hypergraphs with countable Borel chromatic numbe...
APAL
2011
13 years 5 months ago
2011
We study ideals in the computably enumerable Turing degrees, and their upper bounds. Every proper Σ0 4 ideal in the c.e. Turing degrees has an incomplete upper bound. It follows t...
APAL
2011
13 years 5 months ago
2011
The Suslin operator E1 is a type-2 functional testing for the wellfoundedness of binary relations on the natural numbers. In the context of applicative theories, its proof-theoret...
APAL
2011
13 years 5 months ago
2011
We describe strongly minimal theories Tn with finite languages such that in the chain of countable models of Tn, only the first n models have recursive presentations. Also, we d...
APAL
2011
13 years 5 months ago
2011
We formalize the construction of Paterson’s variant of the Ajtai–Koml´os–Szemer´edi sorting network of logarithmic depth in the bounded arithmetical theory VNC1 ∗ (an ex...