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I've been playing around with these (hyperreals) lately and have a couple questions. One concerns the Archimedean property. I keep finding different formulations of it. Some of them lend themselves to transfer. For example, if the AP is that for every real x there exists positive n such that |x|<n then this transfers nicely. Another formulation stipulates that n is finite which wouldn't transfer. Anywho, I'd like to get the sharp, orthodox take on this.

Question numero 2: So I've seen references to using superstructures and constructing a first order logic on the superstructure so you can talk about things like measures and what not. Now the completeness property of the reals (every bounded subset has...) seems as though it could be phrased in such a logic and then transferred?

I'm sure these questions reveal my naive understanding of the hyperreals. Math gods, be gentle...

thanks

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# Hyperreal question

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