Elliot Glazer(@ElliotGlazer):@JDHamkins So in summary, in the extension of L by \aleph_1 Cohen reals, there is a unique-up-to-isomorphism ℝ-sized countably saturated model of PA, and a unique-up-to-isomorphism ℝ-sized hyperreal field, each without any definable instantiation.

Elliot Glazer

@ElliotGlazer

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Elliot Glazer@ElliotGlazer

2026.10.02 04:39

@JDHamkins So in summary, in the extension of L by \aleph_1 Cohen reals, there is a unique-up-to-isomorphism ℝ-sized countably saturated model of PA, and a unique-up-to-isomorphism ℝ-sized hyperreal field, each without any definable instantiation.