# Sh:601

- Kuhlmann, F.-V., Kuhlmann, S., & Shelah, S. (1997).
*Exponentiation in power series fields*. Proc. Amer. Math. Soc.,**125**(11), 3177–3183. arXiv: math/9608214 DOI: 10.1090/S0002-9939-97-03964-6 MR: 1402868 -
Abstract:

We prove that for no nontrivial ordered abelian group G, the ordered power series field R((G)) admits an exponential, i.e. an isomorphism between its ordered additive group and its ordered multiplicative group of positive elements, but that there is a non-surjective logarithm. For an arbitrary ordered field k, no exponential on k((G)) is compatible, that is, induces an exponential on k through the residue map. This is proved by showing that certain functional equations for lexicographic powers of ordered sets are not solvable. - published version (7p)

Bib entry

@article{Sh:601, author = {Kuhlmann, Franz-Viktor and Kuhlmann, Salma and Shelah, Saharon}, title = {{Exponentiation in power series fields}}, journal = {Proc. Amer. Math. Soc.}, fjournal = {Proceedings of the American Mathematical Society}, volume = {125}, number = {11}, year = {1997}, pages = {3177--3183}, issn = {0002-9939}, doi = {10.1090/S0002-9939-97-03964-6}, mrclass = {12J15 (06F20 12J25 13J05)}, mrnumber = {1402868}, mrreviewer = {Joachim Gr\"ater}, doi = {10.1090/S0002-9939-97-03964-6}, note = {\href{https://arxiv.org/abs/math/9608214}{arXiv: math/9608214}}, arxiv_number = {math/9608214} }