There is No Low Maximal D.C.E. Degree
نویسندگان
چکیده
We show that for any computably enumerable (c.e.) degree a and any low n–c.e. degree l (n ≥ 1), if l < a, then there are n–c.e. degrees a0,a1 such that l < a0,a1 < a and a0 ∨ a1 = a. In particular, there is no low maximal d.c.e. degree.
منابع مشابه
There Are No Maximal Low D.C.E. Degrees
We prove that there is no maximal low d.c.e degree.
متن کاملThere is no low maximal d. c. e. degree - Corrigendum
We give a corrected proof of an extension of the Robinson Splitting Theorem for the d.c.e. degrees. The purpose of this short paper is to clarify and correct the main result and proof contained in [1]. There we gave a simple proof that there exists no low maximal d.c.e. degree. This was obtained as an immediate corollary of the following strengthening of the Robinson Splitting Theorem (Theorem ...
متن کاملTuring Definability in the Ershov Hierarchy
We obtain the first nontrivial d.c.e. Turing approximation to the class of computably enumerable (c.e.) degrees. This depends on the following extension of the splitting theorem for the d.c.e. degrees: For any d.c.e. degree a, any c.e. degree b, if b < a, then there are d.c.e. degrees x0,x1 such that b < x0,x1 < a and a = x0 ∨ x1. The construction is unusual in that it is incompatible with uppe...
متن کاملThe nonisolating degrees are nowhere dense in the computably enumerable degrees
The d.c.e. degrees were first studied by Cooper [5] and Lachlan who showed that there is a proper d.c.e degree, a d.c.e. degree containing no c.e. sets, and that every nonzero d.c.e. degree bounds a nonzero c.e. degree, respectively. The main motivation of research on the d.c.e. degrees is to study the differences between the structures of d.c.e. degrees and Δ2 degrees, and between the structur...
متن کاملThe Strongest Nonsplitting Theorem
Sacks [14] showed that every computably enumerable (c.e.) degree ≥ 0 has a c.e. splitting. Hence, relativising, every c.e. degree has a Δ2 splitting above each proper predecessor (by ‘splitting’ we understand ‘nontrivial splitting’). Arslanov [1] showed that 0′ has a d.c.e. splitting above each c.e. a < 0′. On the other hand, Lachlan [9] proved the existence of a c.e. a > 0 which has no c.e. sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Log. Q.
دوره 46 شماره
صفحات -
تاریخ انتشار 2000