The Axioms are Divine-like beings created by the moon Volition. Conceived by the Independents, followers of Independence, who were fascinated by the idea of Divines that did not require an Excerpt. Axioms, in contrast to Divines, are not focused on human ideals, or benefiting people. They embody single ideas, even more than Divines do.
Because they don't have the idea of people at their core, they can sometimes pose a problem to people who encounter them. The Axiom Bountiful caused considerable damage to the Divine Fleet's ships that wanted to pass it, to land on Quire.
The essence of an Axiom can be altered. When Bountiful was first encountered, it was proposed that it could be made into simply a machine, which could produce a large amount of food for the citizens of the Fleet. Another proposal, and the one which was employed, was changing Bountiful from an Axiom into a Divine, a process that was later repeated by the Method of Apotheosis, though how this was accomplished is not yet known.