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.
Exponential fields and Conway’s omega-map
Alessandro Berarducci;
2023-01-01
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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
1810.03029.pdf
accesso aperto
Descrizione: arXiv articolo
Tipologia:
Documento in Pre-print
Licenza:
Creative commons
Dimensione
248.52 kB
Formato
Adobe PDF
|
248.52 kB | Adobe PDF | Visualizza/Apri |
Berarducci et al. - 2023 - Exponential fields and Conway’s omega-map(3).pdf
non disponibili
Descrizione: Articolo versione editoriale
Tipologia:
Versione finale editoriale
Licenza:
NON PUBBLICO - accesso privato/ristretto
Dimensione
266.03 kB
Formato
Adobe PDF
|
266.03 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
omega-fields-vqr.pdf
accesso aperto
Descrizione: Post-print
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
370.73 kB
Formato
Adobe PDF
|
370.73 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.