**Structures That Are Proper Classes**

In the study of set theory and category theory, it is sometimes useful to consider structures in which the domain of discourse is a proper class instead of a set. These structures are sometimes called **class models** to distinguish them from the "set models" discussed above. When the domain is a proper class, each function and relation symbol may also be represented by a proper class.

In Bertrand Russell's Principia Mathematica, structures were also allowed to have a proper class as their domain.

Read more about this topic: Structure (mathematical Logic), Other Generalizations

### Famous quotes containing the words classes, structures and/or proper:

“Journalists belong in the gutter because that is where the ruling *classes* throw their guilty secrets.”

—Gerald Priestland (b. 1927)

“The philosopher believes that the value of his philosophy lies in its totality, in its structure: posterity discovers it in the stones with which he built and with which other *structures* are subsequently built that are frequently better—and so, in the fact that that structure can be demolished and yet still possess value as material.”

—Friedrich Nietzsche (1844–1900)

“With *proper* attribution, to quote another’s thoughts and words is appropriate; plagiarism, however, is cheating, and it may break copyright law as well.”

—Kenneth G. Wilson (1923)