Gödel's "Dialectica": Abstract and Concrete

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• Eric Faber (DPMMS)
• Thursday 18 February 2016, 14:00-15:00
• CMS, MR13.

If you have a question about this talk, please contact Sean Moss.

Gödel’s “Dialectica” interpretation, published in 1958 in the eponymous journal, is an interpretation of Heyting Arithmetic in a quantifier-free theory of functionals, often called Gödel’s T. In this talk, I will contrast Gödel’s original definition with an abstract approach in category theory. Namely, it turns out that the Dialectica interpretation can be understood in terms of a monad on a certain category of fibrations. This correspondence also relates the Dialectica interpretation to other functional interpretations and type theory. However, as I will point out, the connection has some limitations and is still to be better understood.

This talk is part of the Junior Category Theory Seminar series.

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