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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Definable operations on sets and elimination of imaginaries
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by Jan Holly PDF
Proc. Amer. Math. Soc. 117 (1993), 1149-1157 Request permission

Abstract:

This paper gives a new and constructive proof of Poizat’s theorem that the theory of algebraically closed fields admits elimination of imaginaries. The proof uses ideas of definability for properties and operations on definable sets. In addition, the property of being finite in an algebrically closed field, as well as the property of having a given algebraic dimension are shown to be definable properties.
References
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  • Bruno Poizat, Une thĂ©orie de Galois imaginaire, J. Symbolic Logic 48 (1983), no. 4, 1151–1170 (1984) (French). MR 727805, DOI 10.2307/2273680
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 117 (1993), 1149-1157
  • MSC: Primary 03C60; Secondary 03C10, 03C40, 03C45, 12L05
  • DOI: https://doi.org/10.1090/S0002-9939-1993-1116261-6
  • MathSciNet review: 1116261