8 citations · 22 across the 10 of their papers we have counts for
11 papers
Axiom Beta Implies Elementary Transfinite Recursion
Emanuele Frittaion, Giorgio G. Genovesi
We show that , a weak theory of sets with Axiom Beta, proves the scheme of Elementary, or Transfinite Recursion and can generate, for every set, the corresponding…
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…
On Goodman realizability
Emanuele Frittaion
Goodman's theorem (1976) states that intuitionistic finite-type arithmetic plus the axiom of choice plus the axiom of relativized dependent choice is conservative over Heyting arit…
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…
The strength of the SCT criterion
Emanuele Frittaion, Silvia Steila, Keita Yokoyama
We undertake the study of size-change analysis in the context of Reverse Mathematics. In particular, we prove that the SCT criterion is equivalent to -induction over RCA…
Reverse mathematics, well-quasi-orders, and Noetherian spaces
Emanuele Frittaion, Matt Hendtlass, Alberto Marcone +2
A quasi-order induces two natural quasi-orders on , but if is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Gou…
Reverse Mathematics and initial intervals
Emanuele Frittaion, Alberto Marcone
In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of the initial…
Linear extensions of partial orders and Reverse Mathematics
Emanuele Frittaion, Alberto Marcone
We introduce the notion of τ-like partial order, where τis one of the linear order types ω, ω*, ω+ω*, and ζ. For example, being ω-like means that every element has finitely many pr…