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
Famous quotes containing the words type and/or theory:
“The Republican form of government is the highest form of government; but because of this it requires the highest type of human nature—a type nowhere at present existing.”
—Herbert Spencer (1820–1903)
“It makes no sense to say what the objects of a theory are,
beyond saying how to interpret or reinterpret that theory in another.”
—Willard Van Orman Quine (b. 1908)