کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4662566 | 1633544 | 2007 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Randomness and the linear degrees of computability
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We show that there exists a real α such that, for all reals β, if α is linear reducible to β (α≤ℓβ, previously denoted as ) then β≤Tα. In fact, every random real satisfies this quasi-maximality property. As a corollary we may conclude that there exists no ℓ-complete Δ2 real. Upon realizing that quasi-maximality does not characterize the random reals–there exist reals which are not random but which are of quasi-maximal ℓ-degree–it is then natural to ask whether maximality could provide such a characterization. Such hopes, however, are in vain since no real is of maximal ℓ-degree.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 145, Issue 3, March 2007, Pages 252-257
Journal: Annals of Pure and Applied Logic - Volume 145, Issue 3, March 2007, Pages 252-257