Lecture notes - Model Theory (Math 411) Autumn 2002.

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Lecture notes - Model Theory (Math 411). Autumn 2002. Anand Pillay. December 9, 2002. 1 Notation and review. Let me begin by briefly discussing many-sorted …

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Lecture notes - Model Theory (Math 411)
Autumn 2002.
Anand Pillay
December 9, 2002
1 Notation and review.
Let me begin by brie
y discussing many-sorted structures. Although in most
of the course I will be working with the traditional 1-sorted structures, everything
is valid in the more general context.
By a many-sorted language L (or rather a language for many-sorted structures),
we mean a set S of sorts”, a set R of sorted relation symbols, and
a set F of sorted function symbols. What this means is that each R 2 R comes together with a certain nite sequence (S1; ::; Sn) of sorts where n 1,
and each f 2 F comes together with a sequence (S1; ::; Sn; S) of sorts where
n 0. By the cardinality jLj of L we mean jSj + jRj + jF.
By an L-structure M we mean a family (S(M) : S 2 S) of nonempty sets,
together with, for each R 2 R of sort (S1; ::; Sn) a subset R(M) of S1(M) ::: Sn(M), and for…