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

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

5 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.",

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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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