TY - JOUR
T1 - Splitting and cone avoidance in the D.C.E. degrees
AU - Cooper, S. B.
AU - Li, Angsheng
PY - 2002/9
Y1 - 2002/9
N2 - It is shown that the Cooper splitting theorem for the n-c.e. degrees is not compatible with cone avoidance: For any n > 1, there exist n-c.e. degree a, c.e. degree b such that 0 < b < a and such that for any n-c.e. degrees x, y, if x ∨ y = a, then either b ≤ x or b ≤ y. This provides a new type of elementary difference between the classes of c.e. and d.c.e. degrees, implementable at lower levels of the high/low hierarchy.
AB - It is shown that the Cooper splitting theorem for the n-c.e. degrees is not compatible with cone avoidance: For any n > 1, there exist n-c.e. degree a, c.e. degree b such that 0 < b < a and such that for any n-c.e. degrees x, y, if x ∨ y = a, then either b ≤ x or b ≤ y. This provides a new type of elementary difference between the classes of c.e. and d.c.e. degrees, implementable at lower levels of the high/low hierarchy.
KW - Cone avoidance
KW - Cooper splitting theorem
UR - https://www.scopus.com/pages/publications/0347687556
M3 - 文章
AN - SCOPUS:0347687556
SN - 1006-9283
VL - 45
SP - 1135
EP - 1146
JO - Science in China, Series A: Mathematics
JF - Science in China, Series A: Mathematics
IS - 9
ER -