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CHARACTERIZING THE STRONGLY JUMPTRACEABLE SETS VIA RANDOMNESS
"... Abstract. We show that if a set A is computable from every superlow 1random set, then A is strongly jumptraceable. Together with a result from [9], this theorem shows that the computably enumerable jumptraceable sets are exactly the computably enumerable sets computable from every superlow 1rand ..."
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Abstract. We show that if a set A is computable from every superlow 1random set, then A is strongly jumptraceable. Together with a result from [9], this theorem shows that the computably enumerable jumptraceable sets are exactly the computably enumerable sets computable from every superlow 1random set. We also prove the analogous result for superhighness: a c.e. set is strongly jumptraceable if and only if it is computable from any superhigh random set. Finally, we show that for each cost function c with the limit condition there is a random ∆ 0 2 set Y such that each c.e. set A �T Y obeys c. 1.
The nr.e. degrees: undecidability and Σ1 substructures
, 2012
"... We study the global properties of Dn, the Turing degrees of the nr.e. sets. In Theorem 1.5, we show that the first order theory of Dn is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, Dn is not a Σ1substructure of Dm. 1 ..."
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We study the global properties of Dn, the Turing degrees of the nr.e. sets. In Theorem 1.5, we show that the first order theory of Dn is not decidable. In Theorem 1.6, we show that for any two n and m with n < m, Dn is not a Σ1substructure of Dm. 1
INSIDE THE MUCHNIK DEGREES I: DISCONTINUITY, LEARNABILITY AND CONSTRUCTIVISM
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