Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cutting lemma and Zarankiewicz's problem in distal structures   We establish a cutting lemma for definable families of sets in distal
structures, as well as the optimality of the distal cell decomposition for
definable families of sets on the plane in $o$-minimal expansions of fields.
Using it, we generalize the results in [J. Fox, J. Pach, A. Sheffer, A. Suk,
and J. Zahl. "A semi-algebraic version of Zarankiewicz's problem"] on the
semialgebraic planar Zarankiewicz problem to arbitrary $o$-minimal structures,
in particular obtaining an $o$-minimal generalization of the
Szemer\'edi-Trotter theorem.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: eess