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Davis Yoshida's avatar

Thank you for posting this, I really enjoyed the talk even as a relative layperson.

One question I had was how the lack of categoricity manifests when you don't have CH. Do the different sets which might qualify as the hyperreals differ in any properties we can pick out, or is it just that in such a model there fails to be an isomorphism between different sets which qualify as the hyperreals? If the latter, I'm surprised we care so much about getting to say "the" instead of "a".

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Joseph Shipman's avatar

“The answers provided by PD are better and more uniform and so forth than the corresponding answers provided by V=L, which leads to a vision in contrast of set theory as the land of counterexamples and bad news, while in PD so many things work smoothly.”

This aesthetic judgment may be good, but I don’t know because I have no idea what you mean by “smoothly” vs “bad news”.

As a third alternative, if you assume a Real Valued Measurable Cardinal, do the answers to these questions in descriptive set theory come out more like PD or more like V=L, and how do they compare according to the aesthetic criteria you are using?

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