In
mathematical logic, a definable set is an ''n''-ary
relation on the
domain of a
structure whose elements satisfy some
formula in the
first-order language of that structure. A
set
Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics Mathematics
*Set (mathematics), a collection of elements
*Category of sets, the category whose objects and morphisms are sets and total functions, respectively
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can be defined with or without parameters, which are elements of the domain that can be referenced in the formula defining the relation.
Definition
Let
be a first-order language,
an
-structure with domain
,
a fixed
subset of
, and
a
natural number. Then:
* A set
is ''definable in
with parameters from
'' if and only if there exists a formula