A generalization of the Tarski-Seidenberg theorem, and some nondefinability results

  title={A generalization of the Tarski-Seidenberg theorem, and some nondefinability results},
  author={L. Dries},
  journal={Bulletin of the American Mathematical Society},
  • L. Dries
  • Published 1986
  • Mathematics
  • Bulletin of the American Mathematical Society
This article points out some remarkable facts implicit in the results of Lojasiewicz [LI] and Gabrielov [Ga]. An important consequence of Tarski's work [T] on the elementary theory of the reals is a characterization of the sets which are elementarily definable from addition and multiplication on R. Allowing arbitrary reals as constants, this characterization consists of the identification of the definable sets with the semialgebraic sets. (A semialgebraic subset of R is by definition a finite… Expand
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