# An uncountable J\'{o}nsson algebra in a minimal variety

## TL;DR

This paper constructs a Jónsson algebra of size  in the specific variety of Jf3nsson-Tarski algebras, demonstrating a new example within algebraic structures.

## Contribution

It provides the first known example of an uncountable Jf3nsson algebra in a minimal variety, expanding understanding of algebraic diversity.

## Key findings

- Constructed a -sized Jf3nsson algebra in Jf3nsson-Tarski variety
- Demonstrated existence of uncountable Jf3nsson algebra in minimal variety
- Extended algebraic theory of Jf3nsson algebras

## Abstract

We construct a J\'{o}nsson algebra of cardinality $\omega_1$ in the variety of J\'{o}nsson-Tarski algebras.