Pseudo-jump inversion, upper cone avoidance, and strong jump-traceability
نویسندگان
چکیده
منابع مشابه
Beyond Strong Jump Traceability
Strong jump traceability has been studied by various authors. In this paper we study a variant of strong jump traceability by looking at a partial relativization of traceability. We discover a new subclass H of the c.e. K-trivials with some interesting properties. These sets are computationally very weak, but yet contains a cuppable member. Surprisingly they cannot be constructed using cost fun...
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Let A be c.e. Then A is strongly jump traceable if and only if A is Turing below each superhigh Martin-Löf-random set.
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There are noncomputable c.e. sets, computable from every SJT-hard c.e. set. This yields a natural pseudo-jump operator, increasing on all sets, which cannot be inverted back to a minimal pair or even avoiding an upper cone.
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We show that Sacks’ and Shoenfield’s analogs of jump inversion fail for both ttand wttreducibilities in a strong way. In particular we show that there is a ∆2 set B >tt ∅ ′ such that there is no c.e. set A with A′ ≡wtt B . We also show that there is a Σ 0 2 set C >tt ∅ ′ such that there is no ∆2 set D with D′ ≡wtt C . §
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Recent investigations in algorithmic randomness have lead to the discovery and analysis of the fundamental class K of reals called the K-trivial reals, defined as those whose initial segment complexity is identical with that of the sequence of all 1’s. There remain many important open questions concerning this class, such as whether there is a combinatorial characterization of the class and whe...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2013
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.12.018