Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Tarski's Decidability Problem   This note provides a brief guide to the current state of the literature on
Tarski's problems with emphasis on features that distinguish the approach based
on combinatorial and algorithmic group theory from the topological approach to
Tarski's problem. We use this note to provide corrections to some typos and to
address some misconceptions from the recent report by Z. Sela about the
relations between the concepts and results in the approaches to the Tarski
problems. We were forced to read Sela's papers to be able to address some of
his comments, and found errors in his papers 6, 3 and 4 on Diophantine Geometry
published in GAFA and Israel J. Math. which we mention in Section 4. His
proceedings of the ICM 2002 paper also contains wrong Theorem 6 (to make it
correct one has to change the definition of non-elementary hyperbolic
$\omega$-residually free towers to make them equivalent to our coordinate
groups of regular NTQ systems.)

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The categories of this paper are: econ
29
The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom