On a lattice of relational spaces (reducts) for the order of integers

TL;DR

This paper explores the structure of the lattice of reducts for the integer order, identifying a specific sublattice generated by key relations and discussing open questions in the area.

Contribution

It characterizes a sublattice of the reducts lattice for the integer order and introduces relations that generate this sublattice.

Findings

Identified a sublattice generated by specific relations

Described the structure of the reducts lattice for integers

Proposed open questions for further research

Abstract

We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are proposed.