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About: Constructive set theory     Goto   Sponge   NotDistinct   Permalink

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Type: yago:Artifact100021939yago:Instrumentality103575240yago:Object100002684yago:PhysicalEntity100001930programming languageyago:System104377057yago:Whole100003553yago:WikicatSystemsOfSetTheory New Facet based on Instances of this Class

Constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory.The same first-order language with "" and "" of classical set theory is usually used, so this is not to be confused with a constructive types approach.On the other hand, some constructive theories are indeed motivated by their interpretability in type theories. In addition to rejecting the principle of excluded middle, constructive set theories often require some logical quantifiers in their axioms to be bounded, motivated by results tied to impredicativity.