Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10118835 | Annals of Pure and Applied Logic | 2005 | 13 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Salma Kuhlmann, Saharon Shelah,