Notes on conjunctive and quasi degrees

摘要

In this article we prove the following results: (i) Every hemimaximal set has minimal c(l) -degree, i.e. if B is hemimaximal and A is a c.e. set such that A = (c1) B then either B = (c1) A or A is computable. (ii) The sQ-degree of a c.e. set contains either only one or infinitely many c.e. c-degrees. (iii) If A, B are c.e. cylinders in the same sQ(1)-degree and A (c1) B, then this sQ(1)-degree contains infinitely many c.e. c(1)-degrees.