Strongly minimal expansions of (ℂ, +) definable in o-minimal fields

Assaf Hasson; Piotr Kowalski

doi:10.1112/plms/pdm052

Strongly minimal expansions of (ℂ, +) definable in o-minimal fields

Assaf Hasson, Piotr Kowalski

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4 Scopus citations

Abstract

We characterize those functions f: → definable in o-minimal expansions of the reals for which the structure (,+, f) is strongly minimal: such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy: an algebraically closed field is definable in certain strongly minimal structures which are definable in an o-minimal field.

Original language	English
Pages (from-to)	117-154
Number of pages	38
Journal	Proceedings of the London Mathematical Society
Volume	97
Issue number	1
DOIs	https://doi.org/10.1112/plms/pdm052
State	Published - 1 Jan 2008
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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abstract = "We characterize those functions f: → definable in o-minimal expansions of the reals for which the structure (,+, f) is strongly minimal: such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy: an algebraically closed field is definable in certain strongly minimal structures which are definable in an o-minimal field.",

author = "Assaf Hasson and Piotr Kowalski",

note = "Funding Information: The first author was supported by the EPSRC grant no. EP C52800X 1, and the second author was supported by a MODNET (European Commission Research Training Network) grant and by the Polish grants: KBN no. 2P03A 018 24 and MEN no. N201 032 32/2231",

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AU - Kowalski, Piotr

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N2 - We characterize those functions f: → definable in o-minimal expansions of the reals for which the structure (,+, f) is strongly minimal: such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy: an algebraically closed field is definable in certain strongly minimal structures which are definable in an o-minimal field.

AB - We characterize those functions f: → definable in o-minimal expansions of the reals for which the structure (,+, f) is strongly minimal: such functions must be complex constructible, possibly after conjugating by a real matrix. In particular we prove a special case of the Zilber Dichotomy: an algebraically closed field is definable in certain strongly minimal structures which are definable in an o-minimal field.

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Strongly minimal expansions of (ℂ, +) definable in o-minimal fields

Abstract

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