Constructive Set Theories and their Category-theoretic Models

  title={Constructive Set Theories and their Category-theoretic Models},
  author={Alex Simpson},
We advocate a pragmatic approach to constructive set theory, using axioms based solely on set-theoretic principles that are directly relevant to (constructive) mathematical practice. Following this approach, we present theories ranging in power from weaker predicative theories to stronger impredicative ones. The theories we consider all have sound and complete classes of category-theoretic models, obtained by axiomatizing the structure of an ambient category of classes together with its… CONTINUE READING

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