**Finite Model Theory**

Finite model theory is the area of model theory which has the closest ties to universal algebra. Like some parts of universal algebra, and in contrast with the other areas of model theory, it is mainly concerned with finite algebras, or more generally, with finite σ-structures for signatures σ which may contain relation symbols as in the following example:

- The standard signature for graphs is σ
_{grph}={*E*}, where*E*is a binary relation symbol. - A graph is a σ
_{grph}-structure satisfying the sentences and .

A σ-homomorphism is a map that commutes with the operations and preserves the relations in σ. This definition gives rise to the usual notion of graph homomorphism, which has the interesting property that a bijective homomorphism need not be invertible. Structures are also a part of universal algebra; after all, some algebraic structures such as ordered groups have a binary relation <. What distinguishes finite model theory from universal algebra is its use of more general logical sentences (as in the example above) in place of identities. (In a model-theoretic context an identity *t*=*t'* is written as a sentence .)

The logics employed in finite model theory are often substantially more expressive than first-order logic, the standard logic for model theory of infinite structures.

Read more about this topic: Model Theory

### Famous quotes containing the words finite, model and/or theory:

“Are not all *finite* beings better pleased with motions relative than absolute?”

—Henry David Thoreau (1817–1862)

“I had a wonderful job. I worked for a big *model* agency in Manhattan.... When I got on the subway to go to work, it was like traveling into another world. Oh, the shops were beautiful, we had Bergdorf’s, Bendel’s, Bonwit’s, DePinna. The women wore hats and gloves. Another world. At home, it was cooking, cleaning, taking care of the kids, going to PTA, Girl Scouts. But when I got into the office, everything was different, I was different.”

—Estelle Shuster (b. c. 1923)

“The *theory* of the Communists may be summed up in the single sentence: Abolition of private property.”

—Karl Marx (1818–1883)