Countable homogeneous lattices

TL;DR

This paper demonstrates that there are uncountably many countable lattices and explores their properties related to modularity and distributivity, extending the method to other classes of structures.

Contribution

It establishes the uncountability of countable lattices and analyzes their modular and distributive properties, introducing a method applicable to other structure classes.

Findings

There are uncountably many countable lattices.

Some lattices can be modular or distributive.

The method applies to other classes of structures.

Abstract

We show that there are uncountably many countable lattices. We give a discussion of which such lattices can be modular or distributive. The method applies to show that certain other classes of structures also have uncountably many homogeneous structures