Abstract
We explain how the field of logarithmic-exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential-logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Th(R{double-struck} an, exp the elementary theory of the ordered field of real numbers, with the exponential function and restricted analytic functions.
| Original language | English |
|---|---|
| Pages (from-to) | 434-448 |
| Number of pages | 15 |
| Journal | Mathematical Logic Quarterly |
| Volume | 58 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Nov 2012 |
Keywords
- Exponential closure
- Exponential extension
- Generalized power series
- Growth axioms
- Hahn groups
- Morphisms of prelogarithmic fields
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