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AML
2006

The Medvedev lattice of computably closed sets

13 years 3 months ago
The Medvedev lattice of computably closed sets
Simpson introduced the lattice P of 0 1 classes under Medvedev reducibility. Questions regarding completeness in P are related to questions about measure and randomness. We present a solution to a question of Simpson about Medvedev degrees of 0 1 classes of positive measure that was independently solved by Simpson and Slaman. We then proceed to discuss connections to constructive logic. In particular we show that the dual of P does not allow an implication operator (i.e. that P is not a Heyting algebra). We also discuss properties of the class of PA-complete sets that are relevant in this context.
Sebastiaan Terwijn
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2006
Where AML
Authors Sebastiaan Terwijn
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