6 papers
Strong completeness of the logic J
Juan P. Aguilera, Grigorii Stepanov
We prove that the polymodal logic is strongly complete with respect to \textit{-bouquets}, a topological refinement of its Kripke semantics. In particular,…
Conditionals and Modalities in Constructive Quantum Logics
Juan P. Aguilera, Guillaume Massas
We investigate logics that generalize both intuitionistic logic and quantum logic. In earlier work, we introduced Ex-logic, an extension of Holliday's fundamental logic that coinci…
The Provably Total Set-Recursive Functions of KPl
Juan Pablo Aguilera, Anton Fernández, Joost J. Joosten
Using relativized ordinal analysis, we give a proof-theoretic characterization of the provably total set-recursive-from- functions of KPl and related theories.
Constructive Quantum Logics
Juan P. Aguilera, Guillaume Massas
Following a suggestion of Birkhoff and Von Neumann [Ann. Math. 37 (1936), 23-32], we pursue a joint study of quantum logic and intuitionistic logic. We exhibit a linear-time transl…
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 c…
On some subtheories of strong dependent choice
Juan P. Aguilera, Yudai Suzuki, Keita Yokoyama
In this paper, we give characterizations of the set of -consequences, -consequences and -consequences of the axiomatic system of the stron…