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Tagged with elementary-proofs theories-of-arithmetic
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Which part(s) of this proof of Goodstein's Theorem are not expressible in Peano arithmetic?
EDIT: Noah Schweber helpfully points out that $\mathsf{ACA}_0$ is a conservative extension of Peano arithmetic in which certain aspects of my proof not expressible in Peano arithmetic are expressible. ...
- 708
10
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Minkowski's lattice theorem in fragments of arithmetic
It is widely remarked that Minkowski's lattice theorem (or, convex body theorem) is a kind of geometrical pigeonhole principle. And it seems it should have a very elementary proof at least for convex ...
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