Recursive linear orders with recursive successivities

Abstract

A successivity in a linear order is a pair of elements with no other elements between them. A recursive linear order with recursive successivities $\text{U}$ is recursively categorical if every recursive linear order with recursive successivities isomorphic to $\text{U}$ is in fact recursively isomorphic to $\text{U}$. We characterize those recursive linear orders with recursive successivities that are recursively categorical as precisely those with order type k₁+g₁+k₂+g₂+…+g_n-1+k_n where each k_n is a finite order type, non-empty for iϵ{2,…,n-1} and each g_i is an order type from among {ω,ω^*,ω+ω^*}∪{k·η:k<ω}.