We show that in the c.e. weak truth table degrees if b < c then there is an a which contains no hypersimple set and b < a < c. We also show that for every w < c in the c.e. wtt degrees such that w is hypersimple, there is a hypersimple a such that w < a < c. On the other hand, we know that there are intervals which contain no hypersimple set.
"The Hypersimple-Free C.E. WTT Degrees Are Dense in the C.E. WTT Degrees." Notre Dame J. Formal Logic 47 (3) 361 - 370, 2006. https://doi.org/10.1305/ndjfl/1163775443