Gap-languages and log-time complexity classes

This paper shows that classical results about complexity classes involving "delayed diagonalization" and "gap languages", such as Ladner's Theorem and Schöning's Theorem and independence results of a kind noted by Schöning and Hartmanis, apply at very low levels of complexity, indeed all the way down in Sipser's log-time hierarchy. This paper also investigates refinements of Sipser's classes and notions of log-time reductions, following on from recent work by Cai, Chen, and others.