RECURSIVE LINEAR ORDERS WITH INCOMPLETE SUCCESSIVITIES

A recursive linear order is said to have intrinsically complete successivities if, in every recursive copy, the successivities form a complete set. We show (Theorem 1) that there is a recursive linear order with intrinsically complete successivities but (Theorem 2) that this cannot be a discrete linear oder. We investigate the related issues of intrinsically non-low and non-semi-low successivities in discrete linear orders. We show also (Theorem 3) that no recursive linear order has intrinsically wtt-complete successivities.