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}
}
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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SHOWING 1-10 OF 36 REFERENCES

The consistency of classical set theory relative to a set theory with intuitionistic logic

  • H. Friedman
  • Journal of Symbolic Logic,
  • 1973
Highly Influential
15 Excerpts

Ŝĉedrov. The lack of definable witnesses and provably recursive functions in intuitionistic set theories

  • A. H. Friedman
  • Advances in Mathematics,
  • 1985
Highly Influential
5 Excerpts

Normalization of IZF with Replacement

  • W. Moczydłowski
  • In Proc. 15th Ann. Conf. of the EACSL (CSL ),
  • 2006
Highly Influential
9 Excerpts

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