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The algebraic numbers definable in various exponential fields

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The algebraic numbers definable in various exponential fields. / Kirby, J; Macintyre, Angus; Onshuus, Alf.

In: Journal of the Institute of Mathematics of Jussieu, Vol. 11, No. 4, 2012, p. 825-834.

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Kirby, J ; Macintyre, Angus ; Onshuus, Alf. / The algebraic numbers definable in various exponential fields. In: Journal of the Institute of Mathematics of Jussieu. 2012 ; Vol. 11, No. 4. pp. 825-834.

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@article{c45a7d81a83a47a1a2baa3dd0469d9bd,
title = "The algebraic numbers definable in various exponential fields",
abstract = "We prove the following theorems. Theorem 1: for any E-field with cyclic kernel, in particular C or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: for the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers.",
author = "J Kirby and Angus Macintyre and Alf Onshuus",
year = "2012",
doi = "10.1017/S1474748012000047",
language = "English",
volume = "11",
pages = "825--834",
journal = "Journal of the Institute of Mathematics of Jussieu",
issn = "1474-7480",
publisher = "Cambridge University Press",
number = "4",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - The algebraic numbers definable in various exponential fields

AU - Kirby, J

AU - Macintyre, Angus

AU - Onshuus, Alf

PY - 2012

Y1 - 2012

N2 - We prove the following theorems. Theorem 1: for any E-field with cyclic kernel, in particular C or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: for the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers.

AB - We prove the following theorems. Theorem 1: for any E-field with cyclic kernel, in particular C or the Zilber fields, all real abelian algebraic numbers are pointwise definable. Theorem 2: for the Zilber fields, the only pointwise definable algebraic numbers are the real abelian numbers.

U2 - 10.1017/S1474748012000047

DO - 10.1017/S1474748012000047

M3 - Article

VL - 11

SP - 825

EP - 834

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

SN - 1474-7480

IS - 4

ER -

ID: 625129