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math.LO2024
Induction on Dilators and Bachmann-Howard Fixed Points
Juan P. Aguilera, Anton Freund, Andreas Weiermann
One of the most important principles of J.-Y. Girard's -logic is induction on dilators. In particular, Girard used this principle to construct his famous functor . He cla…
math.LO2024
Fraïssé's conjecture, partial impredicativity and well-ordering principles, part I
Anton Freund
Fraïssé's conjecture (proved by Laver) is implied by the -comprehension axiom of reverse mathematics, as shown by Montalbán. The implication must be strict for reasons of qu…
math.LO2024
Dilators and the reverse mathematics zoo
Anton Freund
A predilator is a particularly uniform transformation of linear orders. We have a dilator when the transformation preserves well-foundedness. Over the theory from…