A splitting theorem for π-π πΈπ΄ degrees
Richard A. Shore, Theodore A. Slaman Β· Proceedings of the American Mathematical Society Β· 2001
We prove that, for any D D , A A and U U with D > T A β U D>_{T}A\oplus U and r.e., in A β U A\oplus U , there are pairs X 0 , X 1 X_{0},X_{1} and Y 0 , Y 1 Y_{0},Y_{1} such that D β‘ T X 0 β X 1 D\equiv _{T}X_{0}\oplus X_{1} ; D β‘ T Y 0 β Y 1 D\equiv _{T}Y_{0}\oplus Y_{1} ; and, for any i i and j