kappa-bounded Exponential-Logarithmic Power Series Fields
| Autor: | Salma Kuhlmann, Saharon Shelah |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Power series
Logarithm Logic Logarithmic rank 0102 computer and information sciences Commutative Algebra (math.AC) 01 natural sciences msc:03C60 Models of real exponentiation FOS: Mathematics ddc:510 0101 mathematics Mathematics 010102 general mathematics Mathematical analysis Mathematics - Logic Mathematics - Rings and Algebras Mathematics - Commutative Algebra Exponential function Mathematics::Logic 010201 computation theory & mathematics Rings and Algebras (math.RA) Bounded function msc:06A05 Iterated lexicographic power of a chain Logic (math.LO) |
| DOI: | 10.48550/arxiv.math/0512220 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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