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Tesi etd-11232019-091151


Thesis type
Tesi di laurea magistrale
Author
FRENI, PIETRO
email address
pietro.freni@hotmail.it
URN
etd-11232019-091151
Title
Surreal numbers, Transseries and Omega maps
Struttura
MATEMATICA
Corso di studi
MATEMATICA
Commissione
relatore Prof. Berarducci, Alessandro
Parole chiave
  • ordered
  • surreal
  • transseries
  • logic
  • omega
  • exponential
  • logarithmic
  • logarithm
  • field
Data inizio appello
13/12/2019;
Consultabilità
secretata d'ufficio
Riassunto analitico
We prove the ordered abelian group of monomials of the field of logarithmic exponential transseries is isomorphic to the additive reduct of the field itself and describe such an isomorphism (omega map); then discuss its relation with Conway's omega map on surreal numbers. In the process, a way of defining a "bounded version" of Hahn fields, starting from some additionl "bound" data, is described, and a decomposition theorem for the group of monomials of transseries is proven.
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