کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4662018 1633487 2012 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The high/low hierarchy in the local structure of the ωω-enumeration degrees
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
پیش نمایش صفحه اول مقاله
The high/low hierarchy in the local structure of the ωω-enumeration degrees
چکیده انگلیسی

This paper gives two definability results in the local theory of the ωω-enumeration degrees. First, we prove that the local structure of the enumeration degrees is first order definable as a substructure of the ωω-enumeration degrees. Our second result is the definability of the classes HnHn and LnLn of the highnn and lown ωω-enumeration degrees. This allows us to deduce that the first order theory of true arithmetic is interpretable in the local theory of the ωω-enumeration degrees.


► We prove that each nonzero Δ20 e-degree is cupped by a member of a KK-pair, splitting 0e′.
► We characterize the KK-pairs in the local structure of the ωω-enumeration degrees, GωGω.
► We prove that for every nn, the degree on is first order definable in GωGω.
► We prove that an isomorphic copy of the Σ20 e-degrees is definable in GωGω.
► We prove that every level of the high/low jump hierarchy is definable in GωGω.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 163, Issue 5, May 2012, Pages 547–566
نویسندگان
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