How can the theory of real numbers be decidable while Peano arithmetic is not? Why can't Godel numbering be used to demonstrate a true but unprovable sentence given that the natural numbers that are needed to construct such a sentence are subset of the real numbers, so a fortiori, from the stronger reason that PA is undecidable, the theory of real numbers must be as well. But that apparently isn't true and I'm wondering - why not?
2026-02-24 08:20:34.1771921234
Theory of real numbers is decidable but Peano arithmetic is undecidable?
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