A report on Tarski's decidability problem
Z. Sela
TL;DR
This paper critically examines and corrects errors in a previous influential work on the elementary theory of free nonabelian groups, highlighting mistakes and providing counterexamples to key claims.
Contribution
It identifies and rectifies significant errors in Kharlampovich and Myasnikov's 2006 paper, clarifying the decidability status of Tarski's problem.
Findings
Revealed crucial mistakes in the original paper
Provided counterexamples to key statements
Clarified the correct understanding of Tarski's decidability problem
Abstract
This paper contains a list of crucial mistakes and counterexamples to some of the main statements in the paper "Elementary theory of free nonabelian groups" by O. Kharlampovich and A. Myasnikov, which was published in the Journal of Algebra in June 2006.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Logic, programming, and type systems · semigroups and automata theory