Type of Publication: | Preprint |
URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-212455 |
Author: | D'Aquino, Paola; Knight, Julia F.; Kuhlmann, Salma; Lange, Karen |
Year of publication: | 2011 |
ArXiv-ID: | arXiv:1112.4062 |
Summary: |
In an extended abstract Ressayre considered real closed exponential fields and integer parts that respect the exponential function. He outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre's construction, which becomes canonical once we fix the real closed exponential field, a residue field section, and a well ordering of the field. The procedure is constructible over these objects; each step looks effective, but may require many steps. We produce an example of an exponential field $R$ with a residue field $k$ and a well ordering $<$ such that $D^c(R)$ is low and $k$ and $<$ are $\Delta^0_3$, and Ressayre's construction cannot be completed in $L_{\omega_1^{CK}}$.
|
Subject (DDC): | 510 Mathematics |
Comment on publication: | Also publ. in: Fundamenta Mathematicae ; 219 (2012), 2. - S. 163-190 |
Link to License: | In Copyright |
Bibliography of Konstanz: | Yes |
D'AQUINO, Paola, Julia F. KNIGHT, Salma KUHLMANN, Karen LANGE, 2011. Real Closed Exponential Fields
@unpublished{DAquino2011Close-21245, title={Real Closed Exponential Fields}, year={2011}, author={D'Aquino, Paola and Knight, Julia F. and Kuhlmann, Salma and Lange, Karen}, note={Also publ. in: Fundamenta Mathematicae ; 219 (2012), 2. - S. 163-190} }
daquino_212455.pdf | 124 |