# Three Different Formalisations of Einstein's Relativity Principle

## TL;DR

This paper explores three formal definitions of Einstein's special relativity principle, analyzing their logical relationships and showing how they can be made equivalent with minimal additional axioms.

## Contribution

It introduces three distinct formalizations of Einstein's relativity principle and demonstrates their logical relationships and conditions for equivalence.

## Key findings

- The three formalizations are logically distinct.
- They can be made equivalent with a few additional axioms.
- The relationships between the formalizations are explicitly characterized.

## Abstract

We present three natural but distinct formalisations of Einstein's special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms.