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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Some model theory of compact Lie groups
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by Ali Nesin and Anand Pillay PDF
Trans. Amer. Math. Soc. 326 (1991), 453-463 Request permission


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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 326 (1991), 453-463
  • MSC: Primary 03C40; Secondary 03C60, 22E15
  • DOI:
  • MathSciNet review: 1002922