the volume suitable to serve both as an introduction to current research in the field
and as a reference text.
In spite of the title of this book, not all the articles deal with finite combinatorics
in a strict sense. Two articles deal with countable homogeneous and countable
universal structures, one article deals with partition properties of group actions,
and two articles explore various aspects of Ramsey’s Theorem. Still, they all share
a model theoretic view and involve notions from finite Combinatorics.
Two applications of Model Theory to Combinatorics are, unfortunately, not
covered in this volume, as they were published, or promised for publication else-
where, before this volume came into being. G. Elek and B. Szegedy6 used ul-
traproducts and Loeb measures to prove generalizations of Szemer´ edi’s Regularity
Lemma to hypergraphs. The Regularity Lemma plays a crucial ole in the study of
very large finite graphs. A. Razborov7 used Model Theory to develop flag algebras,
which allow one to derive results in extremal graph theory in a uniform way.
The volume is the outcome of the special session on
Model Theoretic Methods in Finite Combinatorics
that was held at the AMS-ASL Meeting of January 2009 in Washington D.C.
Most speakers of the special session, and a few other prominent researchers in
the area, were invited to contribute to the volume. In the name of all the authors
we would like to thank the referees for their careful reading of the contributions
and their many suggestions which were incorporated into the final articles. Spe-
cial thanks go to Christine Thivierge at the American Mathematical Society for
patiently shepherding us through the publication process.
Martin Grohe
Johann Makowsky
Elek and B. Szegedy, Limits of hypergraphs, removal and regularity lemmas. A non-
standard approach, Available at: arXiv: 0705.2179, 2007.
Razborov, Flag algebras, Journal of Symbolic Logic 72.4 (2007), 1239–1282.
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