# A Dependent Set Theory

@article{Moczydlowski2007ADS, title={A Dependent Set Theory}, author={Wojciech Moczydlowski}, journal={22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)}, year={2007}, pages={23-34} }

- Published in 22nd Annual IEEE Symposium on Logic in Computer…2007
DOI:10.1109/LICS.2007.7

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