A Dependent Set Theory

  title={A Dependent Set Theory},
  author={Wojciech Moczydlowski},
  journal={22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)},
Set theories are traditionally based on first-order logic. We show that in a constructive setting, basing a set theory on a dependent logic yields many benefits. To this end, we introduce a dependent impredicative constructive set theory which we call IZFD. Using realizability, we prove that the underlying lambda calculus weakly normalizes, thus enabling program extraction from IZF_D proofs. We also show that IZFD can interpret IZF with Collection. By a wellknown result of Friedman, this… CONTINUE READING

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