Domain of individuals (in logic)

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

$$L=\{P_0,\ldots,P_n,\ldots,F_0,\ldots,F_m,\ldots\}$$

where $P_0,\ldots,P_n,\ldots,$ are predicate symbols and $F_0,\ldots,F_m,\ldots,$ are function symbols for each of which a number of argument places is given. A model $\mathfrak M$ (or an algebraic system) of $L$ is given by a non-empty set $M$ and an interpreting function $I$, defined on $L$ and assigning an $n$-place predicate to an $n$-place predicate symbol, i.e. a subset of the Cartesian power $M^n$ of $M$, and an $n$-place function $M^n\to M$ to an $n$-place function symbol. The set $M$ is called the domain of individuals (or universe) of the model $\mathfrak M$.

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