The fact that people get hung up on the truth or falsehood of set theoretic axioms like Choice or CH is a weird messy holdout of mathematical platonism and we should be taking Godel's completeness theorem more seriously. (No, not his incompleteness theorem. The other one)https://twitter.com/nex3/status/1199086783222255616 …
Wait I haven’t done this stuff in 35 years, but the nonstandard reals are a model for the reals axioms, and not isomorphic, right? Or am i misremembering?
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The nonstandard reals are not a model for the real axioms - they don't satisfy the completeness property. They satisfy all the same first-order sentences, but the real axioms involve quantifying over sets of reals, which is not a first order sentence.
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Ugh, it’s been a long time… if you go beyond fopc, you’ve got a ton of big new philosophical problems if my memory isn’t completely rotten
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