LINEAR ORDERS WITH FINITELY MANY DESCENDING CUTS
Asher M. Kach, Joseph S. Miller · 2008
We show that if L is a lown linear order with only finitely many descending cuts, then L has a computable copy. We also show that neither hypothesis can be weakened: there is a linear order of intermediate degree with a single descending cut and a low3 linear order with infinitely many descending cuts in order type !, neither of which is computable.