A minimalist two-level foundation for constructive mathematics

@article{Maietti2009AMT,
  title={A minimalist two-level foundation for constructive mathematics},
  author={Maria Emilia Maietti},
  journal={Ann. Pure Appl. Logic},
  year={2009},
  volume={160},
  pages={319-354}
}
We present a two-level theory to formalize constructive mathematics as advocated in a previous paper with G. Sambin [MS05]. One level is given by an intensional type theory, called Minimal type theory. This theory extends the set-theoretic version previously introduced in [MS05] with collections. The other level is given by an extensional set theory which is interpreted in the first one by means of a quotient model. This two-level theory has two main features: it is minimal among the most… CONTINUE READING