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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some model theory of compact Lie groups


Authors: Ali Nesin and Anand Pillay
Journal: Trans. Amer. Math. Soc. 326 (1991), 453-463
MSC: Primary 03C40; Secondary 03C60, 22E15
MathSciNet review: 1002922
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Abstract: We consider questions of first order definability in a compact Lie group $ G$. Our main result is that if such $ G$ is simple (and centerless) then the Lie group structure of $ G$ is first order definable from the abstract group structure. Along the way we also show (i) if $ G$ is non-Abelian and connected then a copy of the field $ \mathbb{R}$ is interpretable. in $ (G, \cdot)$, and (ii) any "$ 1$-dimensional" field interpretable in $ (\mathbb{R}, +, \cdot)$ is definably (i.e., semialgebraically) isomorphic to the ground field $ \mathbb{R}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1002922-9
PII: S 0002-9947(1991)1002922-9
Article copyright: © Copyright 1991 American Mathematical Society