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Section: New Results

Mutual interpretability of cartesian planes with Tarski's system of geometry

Participants : Pierre Boutry, Cyril Cohen.

A previous result by Pierre Boutry is that cartesian planes over pythagorean ordered fields are mutually interpretable with Tarski's system of geometry without the continuity axiom. This result can be extended by linking cartesian planes over real closed fields and the full Tarski system of geometry, understanding the continuity axiom as an implementation of Dedekind cuts. On the one hand, this requires a new proof that is not already found in the literature, on the other hand, this will result in a verified quantifier elimination procedure for Tarski's system of geometry, thus extending previous work by Cyril Cohen.