Type of Publication:  Preprint 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352212455 
Author:  D'Aquino, Paola; Knight, Julia F.; Kuhlmann, Salma; Lange, Karen 
Year of publication:  2011 
ArXivID:  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. 163190 
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@unpublished{DAquino2011Close21245, title={Real Closed Exponential Fields}, year={2011}, author={D'Aquino, Paola and Knight, Julia F. and Kuhlmann, Salma and Lange, Karen},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. 163190} }
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