Alfred Tarski’s great algorithm. Decidability of elementary algebra and geometry

On of the most important decidability results is Tarski Theorem. It allows us to determine whether a closed first-order
formula with real variables is true or not. As a corollary we get the decidability of elementary geometry. The original
proof given by Tarski was very involved. After that it was simplified by many researchers. In my talk I am to present
a version of this algorithm which is