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math.LO2024
Choice and independence of premise rules in intuitionistic set theory
Emanuele Frittaion, Takako Nemoto, Michael Rathjen
Choice and independence of premise principles play an important role in characterizing Kreisel's modified realizability and Gödel's Dialectica interpretation. In this paper we show…
math.LO2024
Peano Arithmetic, games and descent recursion
Emanuele Frittaion
We analyze Coquand's game-theoretic interpretation of Peano Arithmetic through the lens of elementary descent recursion. In Coquand's game semantics, winning strategies correspond…
math.LO2024
Iterating reflection over intuitionistic arithmetic
Emanuele Frittaion
In this note, we investigate iterations of consistency, local and uniform reflection over (Heyting Arithmetic). In the case of uniform reflection, we give a new proof…