The real field with convergent generalized power series

Lou van den Dries, Patrick Speissegger

Research output: Contribution to journalArticlepeer-review


We construct a model complete and o-minimal expansion of the field of real numbers in which each real function given on [0,1] by a series ∑cnxαn with 0 ≤ αn → ∞ and ∑ |cn|rαn < ∞ for some r > 1 is definable. This expansion is polynomially bounded.

Original languageEnglish (US)
Pages (from-to)4377-4421
Number of pages45
JournalTransactions of the American Mathematical Society
Issue number11
StatePublished - Dec 1 1998


  • Blowing-up
  • Model completeness
  • O-minimal structures
  • Power series

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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