# A Decision Method For Elementary Algebra And Geometry

@inproceedings{Tarski1951ADM, title={A Decision Method For Elementary Algebra And Geometry}, author={Alfred Tarski}, year={1951} }

By a decision method for a class K of sentence (or other expressions) is meant a method by means of which, given any sentence θ, one can always decide in a finite number of steps whether θ is in K; by a decision problem for a class K we mean the problem of finding a decision method for K. A decision method must be like a recipe, which tells one what to do at each steps so that no intelligence is required to follow it; and the method can be applied by anyone so long as he is able to read and…

## 1,696 Citations

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- 1975

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