Subsets of hypersimple sets

Rodney Graham Downey

Vol. 127 (1987), No. 2, 299–319

DOI: 10.2140/pjm.1987.127.299

Abstract

Structural properties of r.e. sets often have degree theoretic consequences, particularly concerning degrees of supersets. It is our intention to show that such properties can have interesting ramifications on the degrees of subsets, by showing that no hypersimple r.e. set has the universal splitting property (USP). We also show that there are, however, simple sets (indeed, low and promptly simple sets) with USP and thus USP is not invariant under automorphisms of the lattice of r.e. sets.

Mathematical Subject Classification 2000

Primary: 03D25

Milestones

Received: 10 October 1985

Revised: 11 April 1986

Published: 1 April 1987