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Results tagged with surreal-analysis
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user 1946
5
votes
Accepted
What are the properties of $\operatorname{No}[i]$?
The surreal complex field $\text{No}[i]$, known as the surcomplex field, is a proper-class-sized set-saturated algebraically closed field. It is universal for all fields of characteristic 0. Indeed, u …
- 236k
15
votes
Accepted
Can you build the surreal numbers as a simple direct limit of ordered fields?
Here is one way to get a positive answer to the title question.
Theorem. There is a definable class $\mathcal{F}$ of ordered fields, containing isomorphic copies of any given field, and a directed ord …
- 236k
6
votes
Why is it said that all surreal numbers with birthdate $<\omega_1$ are isomorphic to a Hardy...
As Philip Ehrlich had mentioned in the other post, the initial claim of your question is Corollary B of the following paper
Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven, Filling ma …
- 236k