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wuthefwasthat comments on Second order logic, in first order set-theory: what gives? - Less Wrong
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If you believe that there's a unique standard model of the reals, you must also believe that the continuum hypothesis has a definite truth value. Some people don't believe that.
I don't think that's true. You may not believe that the set of functions is unique (in which case the notion of sets in bijection is no longer unique).