5 papers · 1 filter
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…
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…
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…
Extensional realizability for intuitionistic set theory
Emanuele Frittaion, Michael Rathjen
In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring tha…
The strength of SCT soundness
Emanuele Frittaion, Florian Pelupessy, Silvia Steila +1
In this paper we continue the study, from Frittaion, Steila and Yokoyama (2017), on size-change termination in the context of Reverse Mathematics. We analyze the soundness of the S…