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    • CommentRowNumber1.
    • CommentAuthorgbuday
    • CommentTimeFeb 27th 2025
    • (edited Feb 27th 2025)
    I have found only this book reference on categorical logic for higher order logic on Ncatlab:

    https://ncatlab.org/nlab/show/Introduction+to+Higher-Order+Categorical+Logic

    Please tell me if there are others on Ncatlab.

    Also, if you know some new developments in this area after that book. Especially if someone went into the direction of Gordon's HOL, that is with axiom of choice and Hindley-Milner polymorphism.
    • CommentRowNumber2.
    • CommentAuthormaxsnew
    • CommentTimeFeb 27th 2025

    Chapter D4 of Sketches of an Elephant is a good reference on categorical logic for higher-order logic. It discusses the axiom of choice as well.