Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Frittaion, Emanuele"'
Autor:
Frittaion, Emanuele
In "Extensional realizability for intuitionistic set theory", we introduced an extensional variant of generic realizability, where realizers act extensionally on realizers, and showed that this form of realizability provides "inner" models of $\sf CZ
Externí odkaz:
http://arxiv.org/abs/2412.06371
Choice and independence of premise principles play an important role in characterizing Kreisel's modified realizability and G\"odel's Dialectica interpretation. In this paper we show that a great many intuitionistic set theories are closed under the
Externí odkaz:
http://arxiv.org/abs/2411.19907
Autor:
Frittaion, Emanuele
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 to infinitary cut-free proofs and cut elimination corresponds to debat
Externí odkaz:
http://arxiv.org/abs/2411.19884
Autor:
Frittaion, Emanuele
We characterize iterations of consistency, local and uniform reflection over Heyting Arithmetic. The treatment of uniform reflection is based on a proof of Feferman's completeness theorem due to Rathjen. Unlike previous works, this paper does not con
Externí odkaz:
http://arxiv.org/abs/2411.07777
Autor:
Frittaion, Emanuele
We consider fragments of uniform reflection for formulas in the analytic hierarchy over theories of second order arithmetic. The main result is that for any second order arithmetic theory $T_0$ extending ${\sf RCA}_0$ and axiomatizable by a $\Pi^1_{k
Externí odkaz:
http://arxiv.org/abs/2207.11693
Autor:
Frittaion, Emanuele
Publikováno v:
Archive for Mathematical Logic, 59: 715-731 (2020)
Shoenfield's completeness theorem (1959) states that every true first order arithmetical sentence has a recursive $\omega$-proof encodable by using recursive applications of the $\omega$-rule. For a suitable encoding of Gentzen style $\omega$-proofs,
Externí odkaz:
http://arxiv.org/abs/2110.01270
Autor:
Frittaion, Emanuele, Rathjen, Michael
In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving rise to a
Externí odkaz:
http://arxiv.org/abs/2012.04300
Publikováno v:
In Annals of Pure and Applied Logic October-November 2023 174(9)
Autor:
Frittaion, Emanuele
Publikováno v:
Notre Dame J. Formal Logic 60, no. 3 (2019), 523-550
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 arithmetic. The same result applies to the extensional variant. This is du
Externí odkaz:
http://arxiv.org/abs/1801.04968