\newcommand{\etalchar}[1]{$^{#1}$}
\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
% \MRhref is called by the amsart/book/proc definition of \MR.
\providecommand{\MRhref}[2]{%
  \href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
}
\providecommand{\href}[2]{#2}
\begin{thebibliography}{ACGZ20}

\bibitem[ACGZ20]{ACGZ}
Matthias Aschenbrenner, Artem Chernikov, Allen Gehret, and Martin Ziegler,
  \emph{Distality in valued fields and related structures}, arXiv:2008.09889.

\bibitem[BB18]{BB-cohMod}
Martin Bays and Emmanuel Breuillard, \emph{Projective geometries arising from
  {E}lekes-{S}zab{\'o} problems}, arXiv:1806.03422.

\bibitem[BKT04]{BKT}
J.~Bourgain, N.~Katz, and T.~Tao, \emph{A sum-product estimate in finite
  fields, and applications}, Geom. Funct. Anal. \textbf{14} (2004), no.~1,
  27--57. \MR{2053599}

\bibitem[CGS20]{CGS}
Artem Chernikov, David Galvin, and Sergei Starchenko, \emph{Cutting lemma and
  {Z}arankiewicz's problem in distal structures}, Selecta Math. (N.S.)
  \textbf{26} (2020), no.~2, Paper No. 25, 27. \MR{4079189}

\bibitem[CPS]{CPS-ES}
Artem Chernikov, Ya'acov Peterzil, and Sergei Starchenko, \emph{Model-theoretic
  {E}lekes-{S}zab{\'o} for stable and o-minimal hypergraphs}, Forthcoming.

\bibitem[CS15]{CS-extDefII}
Artem Chernikov and Pierre Simon, \emph{Externally definable sets and dependent
  pairs {II}}, Trans. Amer. Math. Soc. \textbf{367} (2015), no.~7, 5217--5235.
  \MR{3335415}

\bibitem[CS18]{CS}
Artem Chernikov and Sergei Starchenko, \emph{A model-theoretic generalization
  of the {E}lekes-{S}zab\'o theorem}, arXiv:1801.09301.

\bibitem[CS20]{CS-ES1d}
\bysame, \emph{Model-theoretic {E}lekes-{S}zab{\'o} in the strongly minimal
  case}, arXiv:1801.09301.

\bibitem[EH91]{EvansHrushovski}
David~M. Evans and Ehud Hrushovski, \emph{Projective planes in algebraically
  closed fields}, Proc. London Math. Soc. (3) \textbf{62} (1991), no.~1, 1--24.
  \MR{1078211}

\bibitem[EP05]{EnglerPrestel}
Antonio~J. Engler and Alexander Prestel, \emph{Valued fields}, Springer
  Monographs in Mathematics, Springer-Verlag, Berlin, 2005. \MR{MR2183496
  (2007a:12005)}

\bibitem[ES12]{ES}
Gy\"orgy Elekes and Endre Szab\'o, \emph{How to find groups? (and how to use
  them in {E}rd\"os geometry?)}, Combinatorica \textbf{32} (2012), no.~5,
  537--571. \MR{3004808}

\bibitem[FPS{\etalchar{+}}17]{FoxEtAl}
Jacob Fox, J\'anos Pach, Adam Sheffer, Andrew Suk, and Joshua Zahl, \emph{A
  semi-algebraic version of {Z}arankiewicz's problem}, J. Eur. Math. Soc.
  (JEMS) \textbf{19} (2017), no.~6, 1785--1810. \MR{3646875}

\bibitem[Hru13]{Hr-psfDims}
Ehud Hrushovski, \emph{On pseudo-finite dimensions}, Notre Dame J. Form. Log.
  \textbf{54} (2013), no.~3-4, 463--495. \MR{3091666}

\bibitem[KSW11]{KSW}
Itay Kaplan, Thomas Scanlon, and Frank~O Wagner, \emph{Artin-{S}chreier
  extensions in {NIP} and simple fields}, Israel Journal of Mathematics
  \textbf{185} (2011), no.~1, 141--153.

\bibitem[Lan02]{Lang-algebra}
Serge Lang, \emph{Algebra}, third ed., Graduate Texts in Mathematics, vol. 211,
  Springer-Verlag, New York, 2002. \MR{MR1878556 (2003e:00003)}

\bibitem[SdZ17]{SZ}
Sophie Stevens and Frank de~Zeeuw, \emph{An improved point-line incidence bound
  over arbitrary fields}, Bull. Lond. Math. Soc. \textbf{49} (2017), no.~5,
  842--858. \MR{3742451}

\bibitem[Sim20]{simon-decomposition}
Pierre Simon, \emph{Type decomposition in {NIP} theories}, J. Eur. Math. Soc.
  (JEMS) \textbf{22} (2020), no.~2, 455--476. \MR{4049222}

\bibitem[TV06]{TaoVu}
Terence Tao and Van Vu, \emph{Additive combinatorics}, Cambridge Studies in
  Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 2006.
  \MR{2289012}

\bibitem[Wei84]{Weispfenning}
Volker Weispfenning, \emph{Quantifier elimination and decision procedures for
  valued fields}, Models and sets ({A}achen, 1983), Lecture Notes in Math.,
  vol. 1103, Springer, Berlin, 1984, pp.~419--472. \MR{775704}

\end{thebibliography}
