FOM: Axiom of infinity
shipman at savera.com
Thu Jul 20 14:33:16 EDT 2000
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
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