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math.LO2026
Initial algebras from constructive ordinals
Benno van den Berg
We show how a standard constructive notion of ordinal supports a useful constructive theory of transfinite recursion. We do this by giving constructive proofs of various initial al…
math.LO2023
Apartness and the elimination of strong forms of extensionality
Benno van den Berg
We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid ver…
math.LO2023
Conservativity of Type Theory over Higher-order Arithmetic
Benno van den Berg, Daniël Otten
We investigate how much type theory is able to prove about the natural numbers. A classical result in this area shows that dependent type theory without any universes is conservati…