Domain of individuals (in logic)
From Encyclopedia of Mathematics
universe
A term in model theory denoting the domain of variation of individual (object) variables of a given formal language of first-order predicate calculus. Each such language is completely described by the set
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where are predicate symbols and
are function symbols for each of which a number of argument places is given. A model
(or an algebraic system) of
is given by a non-empty set
and an interpreting function
, defined on
and assigning an
-place predicate to an
-place predicate symbol, i.e. a subset of the Cartesian power
of
, and an
-place function
to an
-place function symbol. The set
is called the domain of individuals (or universe) of the model
.
References
[1] | S.C. Kleene, "Mathematical logic" , Wiley (1967) |
[2] | C.C. Chang, H.J. Keisler, "Model theory" , North-Holland (1973) |
[3] | Yu.L. Ershov, E.A. Palyutin, "Mathematical logic" , Moscow (1987) (In Russian) |
How to Cite This Entry:
Domain of individuals (in logic). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Domain_of_individuals_(in_logic)&oldid=32761
Domain of individuals (in logic). Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Domain_of_individuals_(in_logic)&oldid=32761
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article