FOM: Axiom of infinity

[Joe Shipman]

Simpson asks for a simple, short axiom of infinity that doesn't
interpret one of the three mentioned by Baldwin (discrete order, dense
order, pairing function).

How about the conjunction of the axioms for a division ring augmented by
the negation of the commutativity axiom for multiplication?  By
Wedderburn's theorem, a finite division ring is a field, so the only
models of this sentence would be infinite.  This is a hard theorem to
prove, so there can't be an easy proof that the sentence interprets one
of the three infinity axioms Baldwin names.

-- Joe Shipman