The algebraic numbers definable in various exponential fields

Jonathan Kirby; Angus Macintyre; Alf Onshuus

doi:10.1017/S1474748012000047

The algebraic numbers definable in various exponential fields

Jonathan Kirby, Angus Macintyre, Alf Onshuus

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	825-834
Number of pages	10
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	11
Issue number	4
DOIs	https://doi.org/10.1017/S1474748012000047
Publication status	Published - 2012

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10.1017/S1474748012000047

Cite this

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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.",

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AU - Macintyre, Angus

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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.

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DO - 10.1017/S1474748012000047

M3 - Article

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SP - 825

EP - 834

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

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