Conjunctive degrees and cylinders

In this article we define and study the notion of a (c,c_1)-cylinder, which turns out to be very useful instrument for investigating the relationships between conjunctive reducibility (c-reducibility) and its injective version c_1-reducibility. Using this notion we prove the following results: (1) Neither hypersimple sets nor hemimaximal sets can be (c,c_1)-cylinders; (2) The c-degree of a noncomputable c.e. set contains either only one or infinitely many noncomputable c_1-degrees; (3) the c-degree of either a hemimaximal set or a hypersimple set contains infinitely many noncomputable c_1-degrees.