General synonyms:
* Postulate: This is a very close synonym, often used interchangeably with "axiom."
* Premise: This emphasizes the idea that an axiom is a starting point for a logical argument.
* Principle: This emphasizes the idea that an axiom is a fundamental truth or rule.
* Truth: This is a simple and straightforward synonym, but it may not always be precise depending on the context.
* Assumption: This highlights the idea that axioms are taken for granted without proof.
More specific synonyms:
* Self-evident truth: This emphasizes the idea that axioms are obvious and do not require proof.
* Fundamental law: This emphasizes the idea that axioms are essential rules governing a system.
* Basic principle: This emphasizes the idea that axioms are foundational concepts.
The best synonym for "axiom" will depend on the specific context and the nuance you want to convey.