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Entity > Abstract > Class > Set

Set
subject			fact

Set	documentation A Class that satisfies extensionality as well as other conditions specified by some choice of set theory. Unlike Classes generally, Sets need not have an associated condition that determines their membership. Rather, they are thought of metaphorically as `built up' from some initial stock of objects by means of certain constructive operations (such as the pairing or power set operations). Note that extensionality alone is not sufficient for identifying Classes with Sets, since some Classes (e.g. Entity) cannot be assumed to be Sets without contradiction
	is first domain of subset
	is second domain of element
	is second domain of subset
	is a kind of Class
Class	has axiom (<=> (instance ?CLASS Class) (subclass ?CLASS Entity))
	has axiom (forall (?INT) (domain disjointDecomposition ?INT Class))
	has axiom (forall (?INT) (domain exhaustiveDecomposition ?INT Class))
	is third domain of domain
	is third domain of domainSubclass
Abstract	is disjoint from Physical

Kinds of Set :

• FiniteSet (3 facts) - A Set containing a finite number of elements
• NullSet (3 facts) - The Set that contains no instances