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Strongly minimal expansions of (ℂ, +) definable in o‐minimal fields
Author(s) -
Hasson Assaf,
Kowalski Piotr
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm052
Subject(s) - mathematics , algebraically closed field , minimal models , minimal model , field (mathematics) , pure mathematics , matrix (chemical analysis) , combinatorics , discrete mathematics , mathematical analysis , chemistry , chromatography
We characterize those functions f :ℂ → ℂ definable in o‐minimal expansions of the reals for which the structure (ℂ,+, 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.