(i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that for any c.e. w, w x implies a ∪ w b ∪ x.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping re...(i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that for any c.e. w, w x implies a ∪ w b ∪ x.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x for each c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extending Harrington's anti-cupping theorem.展开更多
基金supported by“863”project and the National Natural Science Foundation of China.
文摘(i) Call a c.e. degree b anti-cupping relative to x, if there is a c.e. a < b such that for any c.e. w, w x implies a ∪ w b ∪ x.(ii) Call a c.e. degree b everywhere anti-cupping (e.a.c.), if it is anti-cupping relative to x for each c.e. degree x.By a tree method, we prove that every high c.e. degree has e.a.c. property by extending Harrington's anti-cupping theorem.
