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Higher-order Dedekind/Peano axioms are categorical in the sense that they characterize Natural Numbers up to a unique isomorphism. However, there is still a
by ProfHewitt 5y ago
Higher-order Dedekind/Peano axioms are categorical in the
sense that they characterize Natural Numbers up to a unique
isomorphism. However, there is still a proposition about
Natural Numbers that true but unprovable using the
Dedekind/Peano axioms. Further information can be found here:
"Physical Indeterminacy in Digital Computation"
https://papers.ssrn.com/abstract=3459566 https://papers.ssrn.com/abstract=3459566
- syops 5y agoSo the last sentence I made is false. The rest is correct, right?
- ProfHewitt 5y agoYes, the last statement that you made is indeed false, that is, it is not the case that every true proposition is provable in Dededkind's theory.