J. P. Aguilera

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20232026

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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 $Π_{2}^{1}$ -logic is induction on dilators. In particular, Girard used this principle to construct his famous functor $Λ$ . He cla…

math.LO2024

On some subtheories of strong dependent choice

Juan P. Aguilera, Yudai Suzuki, Keita Yokoyama

In this paper, we give characterizations of the set of $Π_{e}^{1}$ -consequences, $Σ_{e}^{1}$ -consequences and $B (Π_{e}^{1})$ -consequences of the axiomatic system of the strong d…