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APAL
2011
10 years 6 months ago
The provably total NP search problems of weak second order bounded arithmetic
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...
Leszek Aleksander Kolodziejczyk, Phuong Nguyen, Ne...
APAL
2011
10 years 6 months ago
The complexity of central series in nilpotent computable groups
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...
Barbara F. Csima, Reed Solomon
APAL
2011
10 years 6 months ago
Stable domination and weight
We develop the theory of domination by stable types and stable weight in an arbitrary theory.
Alf Onshuus, Alexander Usvyatsov
APAL
2011
10 years 6 months ago
Dichotomy theorems for countably infinite dimensional analytic hypergraphs
Abstract. We give classical proofs, strengthenings, and generalizations of Lecomte’s characterizations of analytic ω-dimensional hypergraphs with countable Borel chromatic numbe...
Benjamin D. Miller
APAL
2011
10 years 6 months ago
Upper bounds on ideals in the computably enumerable Turing degrees
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...
George Barmpalias, André Nies
APAL
2011
10 years 6 months ago
The Suslin operator in applicative theories: Its proof-theoretic analysis via ordinal theories
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...
Gerhard Jäger, Dieter Probst
APAL
2011
10 years 6 months ago
New spectra of strongly minimal theories in finite languages
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...
Uri Andrews
APAL
2011
10 years 6 months ago
A sorting network in bounded arithmetic
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...
Emil Jerábek
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