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Results tagged with theories-of-arithmetic
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user 15570
Theories of arithmetic in first-order logic, such as Peano arithmetic, second-order arithmetic, Heyting arithmetic, and their subsystems and extensions. Models of Peano arithmetic.
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Heuristic interpretations of the PA-unprovability of Goodstein's Theorem
I've relatively recently learned about Goodstein's Theorem and its unprovability in Peano arithmetic (the Kirby-Paris Theorem). I do not have any real knowledge of formal logic; but I think I've seen …
- 708
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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. …
- 237k