NullSet Comparison Table

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NullSet comparison table

Subject is an instance of documentation is a kind of have axiom

Set 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 Class
(forall (?INT) (domain exhaustiveDecomposition ?INT Class))

NullSet Set The Set that contains no instances
(=>
(instance ?CLASS MutuallyDisjointClass)
(equal (GeneralizedIntersectionFn ?CLASS) NullSet))

Subject	is an instance of	documentation	is a kind of	have axiom
Set		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	Class	(forall (?INT) (domain exhaustiveDecomposition ?INT Class))
NullSet	Set	The Set that contains no instances		(=> (instance ?CLASS MutuallyDisjointClass) (equal (GeneralizedIntersectionFn ?CLASS) NullSet))

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