A note on the theory of well orders

TL;DR

This paper provides a straightforward proof that the first-order theory of well orders can be fully characterized by transfinite induction and demonstrates that this theory is decidable.

Contribution

It offers a simple proof establishing the axiomatization of well orders' theory via transfinite induction and proves its decidability.

Findings

First-order theory of well orders is axiomatized by transfinite induction.

The theory of well orders is decidable.

Provides a simplified proof of these properties.

Abstract

We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.