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Results tagged with surreal-numbers
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user 83901
For questions about the surreal numbers, which are a real-closed ordered proper-class-sized field that contains both the real numbers and the ordinal numbers. Thus they contain both infinite numbers (including the ordinals, but also infinite numbers like ω-1 and sqrt(ω)) and infinitesimal numbers (like 1/ω). They can also be identified with a subclass of two-player partisan games.
16
votes
Do the surreal numbers enjoy the transfer principle in ZFC?
In $\mathsf{ZFC}$ if any two proper class models of the theory of an infinite set are isomorphic, then global choice holds. This is because $V$ and $\mathrm{Ord}$ are both models of this theory and an …
- 12.4k
5
votes
Accepted
A "surnatural numbers" as a largest model of the natural numbers
I asked (and also answered) a more general version of this question a while ago. To summarize the answer, some results of Kanovei and Shelah have the following corollary:
Fact. In $\mathsf{ZFC}$ there …
- 12.4k