Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.
Exponential fields and Conway's omega-map
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Inspired by Conway's surreal numbers, we study real closed fields whose value group is isomorphic to the additive reduct of the field. We call such fields omega-fields and we prove that any omega-field of bounded Hahn series with real coefficients admits an exponential function making it into a model of the theory of the real exponential field. We also consider relative versions with more general coefficient fields.
fields
math.LO 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
On Conway's Numbers and Games, the Von Neumann Universe, and Pure Set Theory
Surreal numbers can be presented as sets of ordinals with a maximal 'birthday' element, giving a set-theoretic foundation equivalent to Gonshor's sign expansions and Conway's games.