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
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