Model theory investigates the
relationships between mathematical structures ("models") on the one
hand and formal languages (in which statements about these
structures can be formulated) on the other.
are: the natural numbers with the usual arithmetical operations, the
structures familiar from algebra, ordered sets, etc.
is on first-order languages, the model theory of which is best
known. An example result is Löwenheim's theorem (the oldest in
the field): a first-order sentence true of some uncountable
structure must hold in some countable structure as
well. Second-order languages and several of its fragments are dealt
with as well.
As the title indicates, this book introduces the
reader to what is basic in model theory. A special feature is its
use of the Ehrenfeucht game by which the reader is familiarized with
the world of models.