TY - JOUR
T1 - Non-Uniformity and Generalised Sacks Splitting
AU - Cooper, S. Barry
AU - Li, Ang Sheng
PY - 2002/4
Y1 - 2002/4
N2 - We show that there do not exist computable functions f1(e,i), f2(e, i), g1(e,i), g2(e,i) such that for all e, i ∈ w, (1) (Wf1(e,i) - Wf2(e,i)) ≤T (We - Wi); (2) (Wg1(e,i) - Wg2(e,i)) ≤T (We - Wi); (3) (We - Wi) ≤T (Wf2(e,i) - Wf2(e.i)) ⊖ (Wg1(e,i) - Wg2(e,i)); (4) (We - Wi) ≰T (Wf1(e,i) - Wf2(e,i)) unless (We - Wi) ≤T 0 and (5) (We - Wi) ≰T (Wg1(e,i) - Wg2(e,i)) unless (We - Wi) ≤T 0. It follows that the splitting theorems of Sacks and Cooper cannot be combined uniformly.
AB - We show that there do not exist computable functions f1(e,i), f2(e, i), g1(e,i), g2(e,i) such that for all e, i ∈ w, (1) (Wf1(e,i) - Wf2(e,i)) ≤T (We - Wi); (2) (Wg1(e,i) - Wg2(e,i)) ≤T (We - Wi); (3) (We - Wi) ≤T (Wf2(e,i) - Wf2(e.i)) ⊖ (Wg1(e,i) - Wg2(e,i)); (4) (We - Wi) ≰T (Wf1(e,i) - Wf2(e,i)) unless (We - Wi) ≤T 0 and (5) (We - Wi) ≰T (Wg1(e,i) - Wg2(e,i)) unless (We - Wi) ≤T 0. It follows that the splitting theorems of Sacks and Cooper cannot be combined uniformly.
KW - Computably enumerable (c.e.)
KW - Difference of computably enumerable sets (d.c.e., or 2-c.e.)
KW - Splitting and nonsplitting
KW - Turing degrees
UR - https://www.scopus.com/pages/publications/0347068838
U2 - 10.1007/s101140100150
DO - 10.1007/s101140100150
M3 - 文章
AN - SCOPUS:0347068838
SN - 1439-8516
VL - 18
SP - 327
EP - 334
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 2
ER -