APAL

2011

12 years 11 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

12 years 11 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

12 years 11 months ago
2011

We develop the theory of domination by stable types and stable weight in an arbitrary theory.

APAL

2011

12 years 11 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

12 years 11 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

12 years 11 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

12 years 11 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

12 years 11 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...