Sh:857

• Kuhlmann, S., & Shelah, S. (2005). \kappa-bounded exponential-logarithmic power series fields. Ann. Pure Appl. Logic, 136(3), 284–296. arXiv: math/0512220 DOI: 10.1016/j.apal.2005.04.001 MR: 2169687
• Abstract:
  In [KKSh:601] 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 to construct for every \kappa regular uncountable cardinal, 2^{\kappa} pairwise non-isomorphic models of real exponentiation (of cardinality \kappa), but all isomorphic as ordered fields. Indeed, the 2^{\kappa} exponentials constructed have pairwise distinct growth rates. This method relies on constructing lexicographic chains with many automorphisms.
• Version 2005-04-18_10 (14p) published version (13p)

@article{Sh:857,
 author = {Kuhlmann, Salma and Shelah, Saharon},
 title = {{$\kappa$-bounded exponential-logarithmic power series fields}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {136},
 number = {3},
 year = {2005},
 pages = {284--296},
 issn = {0168-0072},
 mrnumber = {2169687},
 mrclass = {03C60 (06A05)},
 doi = {10.1016/j.apal.2005.04.001},
 note = {\href{https://arxiv.org/abs/math/0512220}{arXiv: math/0512220}},
 arxiv_number = {math/0512220}
}