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. Example structures are: the natural numbers with the usual
arithmetical operations, the structures familiar from algebra,
ordered sets, etc. The emphasis is on first-order languages, the
model theory of which is best known. An example result is
Loewenheim'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
their 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 familiarised with the world of models.
General
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