# Assignment (FOL)

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## Contents

## Definition

An *assignment*, [ilmath]\sigma[/ilmath] is a map whose domain is the variable set, [ilmath]V[/ilmath], and the co-domain is the set of a domain^{[1]}.

- If [ilmath]\mathscr{L} [/ilmath] is a first order language, [ilmath]V[/ilmath] the set of variable symbols of [ilmath]\mathscr{L} [/ilmath], and [ilmath]\mathbb{M}:=(M,\mathcal{F},\mathcal{R})[/ilmath] is a domain, then an assignment is a mapping:
- [ilmath]\sigma:V\rightarrow M[/ilmath] is an assignment, is associates with each variable symbol a in the domain.

The set of all assignments is denoted:

- [ilmath][V\rightarrow M][/ilmath]
^{[1]}

## See next

## See also

- Substitution assignment, written [ilmath]\sigma[x_i:=a][/ilmath]
^{[1]}that is the same as [ilmath]\sigma[/ilmath] except it maps the variable [ilmath]x_i[/ilmath] to the value [ilmath]a[/ilmath].

## References

- ↑
^{1.0}^{1.1}^{1.2}Mathematical Logic - Foundations for Information Science - Wei Li