4 ms·
The link to "Peano arithmetic" at the top of the Goodstein page takes you to Peano axioms page. That page says Peano axioms are "close to" second-order arithmet
by daxfohl 3y ago
The link to "Peano arithmetic" at the top of the Goodstein page takes you to Peano axioms page. That page says Peano axioms are "close to" second-order arithmetic, and it also provides an informal distinction between Peano axioms and Peano arithmetic. But there's no wikipedia page for Peano arithmetic.
So I'm curious if this theorem is unprovable in Peano axioms, or just Peano arithmetic. If the latter, then the link at the top of the Goodstein page is rather misleading, unless you're paying close enough attention to notice the blurb about the distinction between Peano axioms and Peano arithmetic.
- thaumasiotes 3y ago> But there's no wikipedia page for Peano arithmetic. But there is such a page. It redirects to https://en.wikipedia.org/wiki/Peano_axioms#Peano_arithmetic_as_first-order_theory https://en.wikipedia.org/wiki/Peano_axioms#Peano_arithmetic_... .
- daxfohl 3y agoOh, I missed that! I'd searched google for the term, and it just returned the top-level Peano axioms page. Anyway, updated the link on the Goodstein's Theorem page to point to that section specifically.