 TOPICS # Structure

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 , .

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.

Structure

## Cite this as:

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