A Cannot understand this corollary on surreal numbers

A
Thread starter Anixx
Start date Mar 15, 2025
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Continuum Set

AI Thread Summary

The corollary states that under the Continuum Hypothesis (CH), every maximal Hardy field is isomorphic to the ordered field of surreal numbers of countable length. This implies a specific relationship between maximal Hardy fields and surreal numbers. The discussion raises a question about whether this means there are no countable surreal numbers greater than the germs of Hardy fields. Clarification on the implications of the corollary regarding the hierarchy of surreal numbers and Hardy fields is sought. Understanding this relationship is crucial for grasping the broader implications of the corollary in the context of surreal numbers.

Mar 15, 2025

Anixx

I cannot understand a corollary from this paper on surreal numbers:

Corollary B. Assuming CH (the Continuum Hypothesis), every maximal Hardy
field is isomorphic as an ordered differential field to the ordered field No(ω1) of
surreal numbers of countable length

Does it say that there are no countable surreal numbers greater than the germs of Hardy fields?

Thread 'Onto set mapping is the surjective set mapping, and into injective?'

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