A splitting theorem for $n-REA$ degrees
نویسندگان
چکیده
منابع مشابه
A SPLITTING THEOREM FOR n−REA DEGREES
We prove that, for any D, A and U with D >T A ⊕ U and r.e. in A⊕ U , there are pairs X0, X1 and Y0, Y1 such that D ≡T X0 ⊕X1; D ≡T Y0 ⊕ Y1; and, for any i and j from {0, 1} and any set B, if Xi ⊕A ≥T B and Yj ⊕ A ≥T B then A ≥T B. We then deduce that for any degrees d, a, and b such that a and b are recursive in d, a 6≥T b, and d is n − REA in a, d can be split over a avoiding b. This shows tha...
متن کاملA non-splitting theorem in the enumeration degrees
We complete a study of the splitting/non-splitting properties of the enumeration degrees below 0′e by proving an analog of Harrington’s non-splitting theorem for the Σ2 enumeration degrees. We show how non-splitting techniques known from the study of the c.e. Turing degrees can be adapted to the enumeration degrees.
متن کاملA Splitting Theorem for Alexandrov Spaces
A classical result of Toponogov [12] states that if a complete Riemannian manifold M with nonnegative sectional curvature contains a straight line, thenM is isometric to the metric product of a nonnegatively curved manifold and a line. We then know that the Busemann function associated with the straight line is an affine function, namely, a function which is affine on each unit speed geodesic i...
متن کاملA Splitting Theorem for Holomorphic Banach Bundles
This paper is motivated by Grothendieck’s splitting theorem. In the 1960s, Gohberg generalized this to a class of Banach bundles. We consider a compact complex manifold X and a holomorphic Banach bundle E → X that is a compact perturbation of a trivial bundle in a sense recently introduced by Lempert. We prove that E splits into the sum of a finite rank bundle and a trivial bundle, provided H(X...
متن کاملA splitting theorem for linear polycyclic groups
We prove that an arbitrary polycyclic by finite subgroup of GL(n,Q) is up to conjugation virtually contained in a direct product of a triangular arithmetic group and a finitely generated diagonal group.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-06015-4