# Dickson's Lemma, Higman's Theorem and Beyond: a survey of some basic results in order theory

## TL;DR

This survey reviews fundamental results in order theory, focusing on proofs that certain orders lack descending chains and antichains, highlighting key theorems like Dickson's Lemma and Higman's Theorem.

## Contribution

It compiles and explains essential proofs of order-theoretic properties, emphasizing their significance and interrelations in the field.

## Key findings

- Orders without descending chains or antichains are characterized.
- Key theorems like Dickson's Lemma and Higman's Theorem are discussed.
- Foundational results in order theory are systematically presented.

## Abstract

We provide proofs for the fact that certain orders have no descending chains and no antichains.