On bQ1$bQ_1$‐degrees of c.e. sets

Abstract

AbstractUsing properties of simple sets we study ‐degrees of c.e. sets. In particular, we prove: (1) If A and B are c.e. sets, A is a simple set and , then there exists a simple set C such that and . (2) the c.e. ‐degrees (‐degrees) do not form an upper semilattice. (3) The c.e. ‐degrees are not dense, but are upwards dense. (4) The ‐degrees are not dense.