Abstract
We give a survey of the model-theoretic approach to algebraically closed fields, algebraic varieties and algebraic groups. Much of what we say is taken quite directly from other sources, specifically [Po 89], [Po 87, Chapter 4], [Bousl 89], and [Pi 89], as well as from basic textbooks on algebraic geometry and algebraic groups ([Sh], [Bor]). As we tend to be brief with our proofs, the reader is advised to look at these other sources for additional details, where appropriate. Also all relevant attributions of results can be found there. The reader should see [Zie] in this volume for ω-stability, imaginaries, canonical bases etc. The present paper can serve as an introduction to naive algebraic geometry for model-theorists, as all the basic notions will be defined.
Author partially supported by a grant from the NSF.
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© 1998 Springer-Verlag Berlin Heidelberg
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Pillay, A. (1998). Model theory of algebraically closed fields. In: Bouscaren, E. (eds) Model Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1696. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68521-0_4
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DOI: https://doi.org/10.1007/978-3-540-68521-0_4
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