Cupping and Diamond Embeddings: A Unifying Approach

摘要

In this paper, we prove that for any nonzero cappable degree c, there is a d.c.e. degree d and a c.e. degree b < d such that c cups d to 0', caps b to 0 and for any c.e. degree w, either w ≤ b or w∨d = 0'. This result has several well-known theorems as direct corollaries, including Arslanov's cupping theorem, Downey's diamond theorem, Downey-Li-Wu's complementation theorem, and Li-Yi's cupping theorem, etc.