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Friedrich Kind
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A Guide Through the Proofs of the Tarski Conjectures
by Benjamin Fine, Anthony Gaglione, Alexei Myasnikov
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After being an open question for sixty years the Tarski conjecture was answered in the affirmative by Olga Kharlampovich and Alexei Myasnikov and independently by Zlil Sela. Both proofs involve long and complicated applications of algebraic geometry over free groups as well as an extension of methods to solve equations in free groups originally developed by Razborov.
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