## Exponentiation in power series fields

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- by Franz-Viktor Kuhlmann, Salma Kuhlmann and Saharon Shelah PDF
- Proc. Amer. Math. Soc.
**125**(1997), 3177-3183 Request permission

## Abstract:

We prove that for no nontrivial ordered abelian group $G$ does the ordered power series field $\mathbb {R}((G))$ admit 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.## References

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## Additional Information

**Franz-Viktor Kuhlmann**- Affiliation: Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany
- Email: fvk@harmless.mathi.uni-heidelberg.de
**Salma Kuhlmann**- Affiliation: Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
- MR Author ID: 293156
**Saharon Shelah**- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@sunrise.huji.ac.il
- Received by editor(s): January 31, 1996
- Received by editor(s) in revised form: May 18, 1996
- Additional Notes: The second author was supported by a Deutsche Forschungsgemeinschaft fellowship. The third author was partially supported by the Edmund Landau Center for research in Mathematical Analysis, and supported by the Minerva Foundation (Germany). Publication number 601.
- Communicated by: Andreas R. Blass
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**125**(1997), 3177-3183 - MSC (1991): Primary 12J15, 06A05; Secondary 12J25, 06F20
- DOI: https://doi.org/10.1090/S0002-9939-97-03964-6
- MathSciNet review: 1402868