On the Elementary Theories of the Muchnik and Medvedev Lattices of Π 01 Classes

Abstract

by Joshua A. Cole Recently, researchers in the foundations of mathematics have become interested in the distributive lattices Pw and Ps, the study of which is a major part of the field of “mass problems.” In general, a mass problem U is a subset of ω (Baire space). We define U ≤s V if there is an index e for a computable functional so that ∀f ∈ V(Φe ∈ U… (More)

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