A discrete linear order with non-dense punctual degrees

Abstract

This paper contributes to a systematic study of punctual structures, which are structures computable without delay. The (punctual) degree structure induced by treating “being primitive recursively isomorphic” as a reduction provides insight into the different speeds of enumerations of a given structure. In this paper, we work towards a classification of density of the punctual degrees for linear orders. More specifically, we construct a discrete linear order whose punctual degrees are not dense.