Why is the name of the main spacecraft "Axiom"?

This is said on the Pixar Wikia:

The literal meaning of the word "Axiom" is something that is taken for granted, reflecting on the population of the Axiom's over-indulgent lifestyle.

However, as a mathematician, I'd like to offer an alternative view of the name (which may have nothing in common with the official reasons for this naming).

Axioms are basic statements of any mathematical theory, that we consider to be true (inside that particular theory) for granted, i.e., without proving them (they cannot be proven, since there are no other statements on which to base any proof). All other statements are built upon them and they are true only as long as the axioms are true.

So, in a way, axioms are origin of every (mathematical) system/theory, and I see the above name as a subtle announcement that this ship (among hundreds of thousands of spacecrafts built to keep humanity safe and happy while Earth was being rejuvenated) will be the origin, as it actually happens to be in the end (the origin from which humans repopulate the Earth).

Edit: The captain's name is B. McCrea. Is it only by accident that "McCrea B." sounds a lot like "McCrib" or is it also a suggestion of the cartoon's finale? It might seem a bit far-fetched, but maybe it's not, considering the other names in the movie. For example, VAQ-M (a vacuuming robot), PR-T ("pretty" hair dresser), L-T (a "light" bot), BIRD-E (golfer with a golfing reference name),... The list with the name explanations is here.

My analysis is as follows:

The Axiom spacecraft is a consistent axiomatic system. This is a formal notion in mathematical logic which states that a particular axiomatic system doesn't imply contradictory statements.

The Axiom space craft is an "axiomatic system" because a "robot" (not a "human") is managing it. Logically the notions of a "robot", an "algorithm" and an "axiomatic system" are very near and theoretically "equivalent" in some contexts of mathematical logic.

Also the Axiom spacecraft is a "consistent" axiomatic system because in some sense it is completely "closed" and "independent" from the environment. Its design allows the inhabitants to live in it without any collapse by internal inconsistency.

The most interesting point here is that it seems the animation designers have a complete knowledge about modern mathematical logic! Particularly about a very technical and famous theorem by Kurt Godel called "Godel's incompleteness theorem" which simply says "every consistent axiomatic system which is sufficiently rich to produce arithmetic is incomplete (i.e. cannot prove all true statements.)" (All of the notions have exact mathematical meanings). A philosophical aspect of this theorem is that no "robot" is "alive" and "life" is not "axiomatizable"!

Note that who are supporting the "life" in the movie.

1. Humans: Who are obviously alive.

2. Wrecked robots: Who are working out of the defined axioms of the boss robot and so they are not a part of algorithm.

3. "Wall-E" and "Eve" (Adam and Eve): Who can feel the "love" which is one of the properties of living beings.

If my analysis is true, Wall-E is one of the deepest movies about philosophy, logic and mathematics! It is a masterwork!

I don't have anything official from the cast or crew. But this Wikia provides a plausible-sounding theory about the name:

The literal meaning of the word "Axiom" is something that is taken for granted, reflecting on the population of the Axiom's over-indulgent lifestyle.

IMDb provides a similar take:

The name of the ship that the humans are living on is "Axiom." In logic and math, an axiom is something unquestionable or taken for granted.