Sufficient conditions for the existence of 0’-limitwise monotonic functions for computable η-like linear orders

Abstract

We find new sufficient conditions for the existence of a 0’-limitwise monotonic function defining the order for a computable η-like linear order L, i.e., of a function G such that L ∑_q∈ℚG(q). Namely, we define the notions of left local maximal block and right local maximal block and prove that if the sizes of these blocks in a computable η-like linear order L are bounded then there is a 0’-limitwise monotonic function G with L = ∑_q∈ℚG(q).