A NEW DECISION METHOD FOR ELEMENTARY ALGEBRA

@article{Seidenberg1954AND,
  title={A NEW DECISION METHOD FOR ELEMENTARY ALGEBRA},
  author={A. Seidenberg},
  journal={Annals of Mathematics},
  year={1954},
  volume={60},
  pages={365}
}
A. Tarski [4] has given a decision method for elementary algebra. In essence this comes to giving an algorithm for deciding whether a given finite set of polynomial inequalities has a solution. Below we offer another proof of this result of Tarski. The main point of our proof is accomplished upon showing how to decide whether a given polynomial f(x, y) in two variables, defined over the field R of rational numbers, has a zero in a real-closed field K containing R.1 This is done in ?2, but for… Expand
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