User blog comment:Edwin Shade/Understanding The Infinite/@comment-80.98.179.160-20171113173859

Tetration is definable.

It's just stuck at epsilon null.

We can't set ω be 0 due to addition, and that ε_0 would be undefined, or 1 due to addition, multiplication and Veblen function's same-valuedness.

But ω is 1 less than 1+ω. Else it would violate the Axiom of Commutativity.