Questions tagged [hardy-fields]

Consider surreal numbers as an H-field with operation of derivation. In such setting for any surreal number $\alpha$ such that $0<\alpha<e^\omega$, $\partial(\alpha)<\alpha$ and for $\alpha&...

In this answer I have encountered with the following statement: Assuming CH, every maximal Hardy field is isomorphic to $(\bf{No}(\omega_1), \partial_{\omega_1})$, where $\bf{No}(\omega_1)$ is the ...

Let us define natural equivalence between elements of Hardy fields and integrals of Dirac comb-like functions. Let us assume a natural embedding of Hardy field into surreal numbers ($[x]=\omega$). ...

This answer refers to $\omega_1$ in context of surreal numbers, and calls it "first uncountable ordinal". But what exactly does it mean? How can it be represented in the $\{L|R\}$ form? How ...