Infinitely More β’ 25 implied HN points β’ 19 Dec 25
- Ultrafinitism holds that only comparatively small or βfeasibleβ numbers exist, and finite arithmetic (FA) formalizes this by axiomatizing arithmetic with a single largest natural number.
- The full theory true in all finite truncation models is not computably axiomatizable, so FA is a distinct and simply stated theory rather than that inexpressible common truncation theory.
- Any model of FA can be interpreted inside a strictly taller FA-model where the former largest number attains much larger values (making previously undefined sums and products defined), revealing a potentialist hierarchy that, when iterated, yields models arising from truncations of bounded induction.