Re: continuum hypothesis and 0=1

Pierre-Yves.Gaillard@xxxxxxxxxxxxxxx a écrit :
What is "being true"?

Now you are playing dense, are you? Or else, I would suggest you get a good book on logic and styudy it before asking all this string of regressive questions

Anyway : in informal terms, "true" (in arithmetic, aka "number theory") is for things like : "Goldbach hypothesis is true", ie for every natural even number >2, there exsts two primes...". GH could be true, but not provable with the current set of axioms for number theory, i.e. ZFC (where integers stand for finite ordinals). For a similar, but easier to check example, "every Goodstein sequence ends at 1" is a sentence of ZFC, and even of the language of Peano axioms; it is provable in ZFC using transfinite induction up to epsilon_0, and not provable in PA, so we say it is true, but...
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Relevant Pages

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