κ-bounded exponential-logarithmic power series fields

Salma Kuhlmann*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In [F.-V. Kuhlmann, S. Kuhlmann, S. Shelah, Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997) 3177-3183] it was shown that fields of generalized power series cannot admit an exponential function. In this paper, we construct fields of generalized power series with bounded support which admit an exponential. We give a natural definition of an exponential, which makes these fields into models of real exponentiation. The method allows us to construct for every κ regular uncountable cardinal, 2κ pairwise non-isomorphic models of real exponentiation (of cardinality κ), but all isomorphic as ordered fields. Indeed, the 2κ exponentials constructed have pairwise distinct growth rates. This method relies on constructing lexicographic chains with many automorphisms.

Original languageEnglish
Pages (from-to)284-296
Number of pages13
JournalAnnals of Pure and Applied Logic
Volume136
Issue number3
DOIs
StatePublished - Nov 2005

Keywords

  • Iterated lexicographic power of a chain
  • Logarithmic rank
  • Models of real exponentiation

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