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Pseudo-exponentiation on algebraically closed fields of characteristic zero

Abstract:
We construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation for the corresponding class of structures and prove that the class has a unique model in every uncountable cardinality. This gives grounds to conjecture that the unique model of cardinality continuum is isomorphic to the field of complex numbers with exponentiation. © 2004 Elsevier B.V. All rights reserved.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1016/j.apal.2004.07.001

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Publisher:
Elsevier B.V. Publisher's website
Journal:
Annals of Pure and Applied Logic Journal website
Volume:
132
Issue:
1
Pages:
67–95
Publication date:
2005-02-05
DOI:
ISSN:
0168-0072
URN:
uuid:b9ffda07-1690-4bc1-b9f7-e6a3f91f7783
Source identifiers:
29483
Local pid:
pubs:29483
Language:
English
Subjects:

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