# Computability in the Lattice of Equivalence Relations

## TL;DR

This paper explores the structure of the lattice of equivalence relations on natural numbers, focusing on the computability aspects and whether certain subclasses form sublattices.

## Contribution

It introduces the concept of subrecursive equivalence relations and examines their lattice-theoretic properties, especially in relation to polynomial-time decidability.

## Key findings

- Identifies conditions under which subclasses form sublattices.
- Analyzes the lattice structure of polynomial-time decidable equivalence relations.
- Provides insights into the computability properties within the lattice.

## Abstract

We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time decidable equivalence relations- form sublattices of the lattice.