Pseudo-exponentiation on algebraically closed fields of characteristic zero

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 conjec...

Full description

Bibliographic Details
Main Author: Zilber, B
Format: Journal article
Language:English
Published: Elsevier 2005
Subjects:
Description
Summary: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.