Let be a language of the first-order
logic. Assume that the language has the following sets of nonlogical symbols:

1. is the set of constant symbols of . (These are nullary function symbols.)

2. is the set of predicate symbols of , and for each ,
is the arity of .
The symbols in
are also called relation symbols of the language .

3. is the set of function symbols of , and for each , is the arity of . The symbols in are also called operation symbols of the language .

4. is the universal
quantifier symbol of .

A structure for
is a tuple ,
, where is a set (called the underlying set of ), and the following hold:

1. For each ,
,

2. For each ,
,

3. For each ,
.

## See also

First-Order Logic,

Lattice
*This entry contributed by Matt Insall
(author's link)*

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## References

Bell, J. L. and Slomson, A. B. *Models and Ultraproducts: an Introduction.* Amsterdam, Netherlands: North-Holland,
1971.Enderton, H. B. *A
Mathematical Introduction to Logic.* New York: Academic Press, 1972.## Referenced
on Wolfram|Alpha

Structure
## Cite this as:

Insall, Matt. "Structure." From *MathWorld*--A Wolfram Web Resource, created by Eric W. Weisstein.
https://mathworld.wolfram.com/Structure.html

## Subject classifications