Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, February 08, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Johann A. Makowsky (Technion, Haifa)

What did Tarski mean with "elementary Geometry is decidable"?

In 1931 Tarski proved the existence of an elimination of quantifiers algorithm for the first order theory of real closed fields. It follows that the first order theory of the reals as an ordered field is decidable. In 1951 and later, Tarski interpreted this result as the decidability of elementary geometry. However, he was aware that it did not clarify the issue of decidability, when all models of Euclidean geometry are taken into account.

In 1980 M. Ziegler proved that the first order theory of pythagorean and euclidean fields is undecidable. This implies that the first order theory of text book geometry is undecidable. In this talk we clarify the situation, and discuss the (un)decidability of various parts of euclidean geometry.

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