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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Definable operations on sets and elimination of imaginaries


Author: Jan Holly
Journal: Proc. Amer. Math. Soc. 117 (1993), 1149-1157
MSC: Primary 03C60; Secondary 03C10, 03C40, 03C45, 12L05
MathSciNet review: 1116261
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1116261-6
PII: S 0002-9939(1993)1116261-6
Keywords: Elimination of imaginaries, algebraically closed field
Article copyright: © Copyright 1993 American Mathematical Society