Pseudo-exponentiation on algebraically closed fields of characteristic zero
type: Item
instance of: scholarly article
title: Pseudo-exponentiation on algebraically closed fields of characteristic zero
zbMATH Open document ID: 1076.03024
published in: Annals of Pure and Applied Logic
publication date: 2005-01-11T00:00:00Z
review text: The author introduces the strongly exponentially-algebraically closed fields with pseudo-ex\-po\-nen\-tia\-tion as structures very close to \(C_{\exp}\), the field of complex numbers with exponentiation, and gives a natural (non first-order) axiomatization for them. One of the main results of the paper is a categoricity theorem stating that there is, up to isomorphism, exactly one such structure of a given uncountable cardinality. It is shown that the well-known Schanuel conjecture and a conjecture stating that certain systems of exponential equations over complex numbers do have solutions in the complex numbers are the conditions under which \(C_{\exp}\) is the corresponding structure of continuum cardinality.
reviewed by: Şerban A. Basarab
Mathematics Subject Classification ID: 03C60
Mathematics Subject Classification ID: 12L12
zbMATH DE Number: 2126478
zbMATH Keywords: exponentiation
zbMATH Keywords: algebraically closed field
zbMATH Keywords: Schanuel conjecture
Wikidata QID: Q56474591
author: Boris Zilber
MaRDI profile type: Publication
OpenAlex ID: W1976209905
cites work: On Schanuel's conjectures
cites work: Q4302493
cites work: Q5316384
cites work: EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE
cites work: COVERS OF THE MULTIPLICATIVE GROUP OF AN ALGEBRAICALLY CLOSED FIELD OF CHARACTERISTIC ZERO
cites work: Q5710731
DBLP publication ID: journals/apal/Zilber05
DOI: 10.1016/J.APAL.2004.07.001
description: scientific article; zbMATH DE number 2126478