Loading...
Please wait, while we are loading the content...
Similar Documents
κ-bounded Exponential-Logarithmic Power Series Fields ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kuhlmann, Salma Shelah, Saharon |
| Abstract | In [K–K–S] 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 κ regular uncountable cardinal, 2 κ pairwise non-isomorphic models of real exponenti-ation (of cardinality κ), but all isomorphic as ordered fields. Indeed, the 2 κ exponentials constructed have pairwise distinct growth rates. This method relies on constructing lexicographic chains with many automorphisms. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0512220v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
