Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Miquel, Alexandre"'
Autor:
Dowek, Gilles, Miquel, Alexandre
We show how to express intuitionistic Zermelo set theory in deduction modulo (i.e. by replacing its axioms by rewrite rules) in such a way that the corresponding notion of proof enjoys the normalization property. To do so, we first rephrase set theor
Externí odkaz:
http://arxiv.org/abs/2310.20253
Autor:
Dowek, Gilles, Miquel, Alexandre
G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this property
Externí odkaz:
http://arxiv.org/abs/2310.20248
Autor:
Maschio, Samuele, Miquel, Alexandre
Publikováno v:
Electronic Notes in Theoretical Informatics and Computer Science, Volume 3 - Proceedings of MFPS XXXIX (November 23, 2023) entics:12426
In this paper we show that using implicative algebras one can produce models of set theory generalizing Heyting/Boolean-valued models and realizability models of (I)ZF, both in intuitionistic and classical logic. This has as consequence that any topo
Externí odkaz:
http://arxiv.org/abs/2310.10576
We continue our work on implicative assemblies by investigating under which circumstances a subset $M \subseteq \mathscr{S}$ gives rise to a lex full subcategory $\mathbf{Asm}_M$ of the quasitopos $\mathbf{Asm}_{\mathcal{A}}$ of all assemblies such t
Externí odkaz:
http://arxiv.org/abs/2306.10120
Implicative algebras, recently discovered by Miquel, are combinatorial structures unifying classical and intuitionistic realizability as well as forcing. In this paper we introduce implicative assemblies as sets valued in the separator of an underlyi
Externí odkaz:
http://arxiv.org/abs/2304.10429
Autor:
Miquel, Alexandre
We prove that all Set-based triposes are implicative triposes.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2011.09085
Publikováno v:
Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2019)
In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of typing rules
Externí odkaz:
http://arxiv.org/abs/1904.08785
Autor:
Berardi, Stefano, Miquel, Alexandre
Publikováno v:
EPTCS 281, 2018
This special issue cover the seventh and last conference of the CL&C series, started in 2006 in San Servolo. Topics are the computational content of logics between intuitionistic logic and classical logic, through normalization, and a new topic, cycl
Externí odkaz:
http://arxiv.org/abs/1810.05392
Autor:
Miquel, Alexandre
Publikováno v:
Math. Struct. Comp. Sci. 30 (2020) 458-510
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this structure is tha
Externí odkaz:
http://arxiv.org/abs/1802.00528
Autor:
Santos, Walter Ferrer, Frey, Jonas, Guillermo, Mauricio, Malherbe, Octavio, Miquel, Alexandre
We consider different classes of combinatory structures related to Krivine realizability. We show, in the precise sense that they give rise to the same class of triposes, that they are equivalent for the purpose of modeling higher-order logic. We cen
Externí odkaz:
http://arxiv.org/abs/1410.5034