Logarithmic-exponential power series

Lou Van Den Dries, Angus Macintyre, David Marker

Research output: Contribution to journalArticlepeer-review


We use generalized power series to construct algebraically a nonstandard model of the theory of the real field with exponentiation. This model enables us to show the undefinability of the zeta function and certain non-elementary and improper integrals. We also use this model to answer a question of Hardy by showing that the compositional inverse to the function (log x)(log log x) is not asymptotic as x → + ∞ to a composition of semialgebraic functions, log and exp.

Original languageEnglish (US)
Pages (from-to)417-434
Number of pages18
JournalJournal of the London Mathematical Society
Issue number3
StatePublished - Dec 1997

ASJC Scopus subject areas

  • Mathematics(all)


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