From the 1 of 4 linked papers with an AI index.
4 papers
Axiom Beta Implies Elementary Transfinite Recursion
Emanuele Frittaion, Giorgio G. Genovesi
The paper introduces a weak set theory called C that includes Axiom Beta and proves elementary (Δ₀) transfinite recursion, allowing the construction of relativized constructible hi…
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…
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 sho…
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…