Interpretability in Type Theory
In 1977 Aczel showed that CZF can be interpreted in Martin-Löf type theory, (using the now consecrated propositions-as-types approach) providing what is now seen a standard model of CZF in type theory. In 1989 Ingrid Lindström showed that non-well-founded sets obtained by replacing the axiom of foundation in CZF with Aczel's anti-foundation axiom (CZFA) can also be interpreted in Martin-Löf type theory.
Read more about this topic: Constructive Set Theory
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