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APAL
2011
13 years 2 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 2 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 2 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...