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Provided the axiom set is recursively enumerable. The second order Peano axioms for the natural numbers are complete.
by yequalsx 15y ago
Provided the axiom set is recursively enumerable. The second order Peano axioms for the natural numbers are complete.
- oelewapperke 15y agoEuhm ... sorry to doubt you here, but it does seem like you're flat-out wrong. Second-order peano arithmetic contains all the axioms you'd need for Godel's proof ... And frankly, though not 100% proved (yet?), it seems to me very clear that any numbering and arithmetic system that contains any form of infinity is doomed to be incomplete. So the only useful arithmetical fields that escape Godel are Zn.