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Results tagged with surreal-numbers
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user 109573
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.
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Do the surreal numbers enjoy the transfer principle in ZFC?
A partial answer to the focused question: it's not provable in ZFC that there is an OD class $\mathbb{Z}^*$ such that $(\mathbb{R}, +, \cdot, \mathbb{Z}) \equiv (\mathrm{No}, +, \cdot, \mathbb{Z}^*).$ …
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