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The model theory of the field of reals with a subgroup of the unit circle

Abstract:
We describe definable sets in the field of reals augmented by a predicate for a finite rank multiplicative group Γ of complex numbers contained in the unit circle . This structure interprets the quotient-space /Γ which, for Γ infinite cyclic, is related to the quantum torus. Every definable set is proved to be a Boolean combination of existentially definable sets. We give a complete set of axioms for the theory of such a structure. © 2008 London Mathematical Society.
Publication status:
Published

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Publisher copy:
10.1112/jlms/jdn037

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
Volume:
78
Issue:
3
Pages:
563-579
Publication date:
2008-11-01
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Source identifiers:
4479
Language:
English
Pubs id:
pubs:4479
UUID:
uuid:54557b50-0e99-44ce-9c6a-68472b37e7cd
Local pid:
pubs:4479
Deposit date:
2012-12-19

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