The low n and low m r . e . degrees are not elementarily equivalent
نویسنده
چکیده
Jockusch, Li and Yang (TAMS 356 (2004), 2557-2568) showed that the Lown and Low1 r.e. degrees are not elementarily equivalent for n > 1. We answer a question they raise by using the results of Nies, Shore and Slaman (PLMS (3) 77 (1998), 241-291) to show that the Lown and Lowm r.e. degrees are not elementarily equivalent for n > m > 1.
منابع مشابه
A Join Theorem for the Computably Enumerable Degrees
It is shown that for any computably enumerable (c.e.) degree w, if w 6= 0, then there is a c.e. degree a such that (a ∨w)′ = a′′ = 0′′ (so a is low2 and a ∨w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low2 c.e. degrees are not elementarily equivalent as partial orderings.
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