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The model theory of the field of reals with a subgroup of the unit circle
Author(s) -
Belegradek Oleg,
Zilber Boris
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn037
Subject(s) - mathematics , quotient , axiom , unit (ring theory) , multiplicative function , discrete mathematics , multiplicative group , unit circle , field (mathematics) , predicate (mathematical logic) , rank (graph theory) , group (periodic table) , combinatorics , pure mathematics , computer science , mathematical analysis , chemistry , mathematics education , geometry , organic chemistry , programming language
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.