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Results tagged with surreal-numbers
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user 17218
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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First-order definable bijection between $P(On)$ (or $No$) and $V$? (Is this equivalent to $V...
It is known that locally one can ``code'' any set in the von Neumann universe $V$ by a set of ordinals. But can one do this globally? In other words, is there a first-order definable bijection $P(On …
- 4,985
9
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answer
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Transcendence degree of the surreals over the subfield generated by the ordinals
Consider the Grothendieck ring $K[\Omega]$ of the semiring $\Omega$ of all ordinals under the operations of natural sum and product. Its quotient field $K(\Omega)$ is naturally a subfield of the order …
- 4,985