Tracing and domination in the Turing degrees
نویسنده
چکیده
We show that if 0′ is c.e. traceable by a, then a is array non-computable. It follows that there is no minimal almost everywhere dominating degree, in the sense of Dobrinen and Simpson [DS04]. This answers a question of Simpson and a question of Nies [Nie09, Problem 8.6.4]. Moreover, it adds a new arrow in [Nie09, Figure 8.1], which is a diagram depicting the relations of various ‘computational lowness’ properties. Finally, it gives a natural definable property, namely nonminimality, which separates almost everywhere domination from highness.
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عنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 163 شماره
صفحات -
تاریخ انتشار 2012