4 citations · 11 across the 14 of their papers we have counts for
17 papers
A topos for extended Weihrauch degrees
Samuele Maschio, Davide Trotta
Weihrauch reducibility is a notion of reducibility between computational problems that is useful to calibrate the uniform computational strength of a multivalued function. It compl…
Fibred sets within a predicative and constructive effective topos
Cipriano Junior Cioffo, Maria Emilia Maietti, Samuele Maschio
We describe the fibrational structure of sets within the predicative variant of Hyland's Effective Topos previously introduced in Feferman's predicat…
Implicative models of set theory
Samuele Maschio, Alexandre Miquel
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 int…
On categorical structures arising from implicative algebras: from topology to assemblies
Samuele Maschio, Davide Trotta
Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (bo…
Implicative models of intuitionistic set theory
Samuele Maschio
In this paper we will show that using implicative algebras one can produce models of intuitionistic set theory generalizing both realizability and Heyting-valued models. This has a…
On posetal and complete partial applicative structures
Samuele Maschio
Every partial applicative structure gives rise to an indexed binary relation, that is a contravariant functor from the category of sets to the category of sets endowed with binary…
Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice
Maria Emilia Maietti, Samuele Maschio, Michael Rathjen
In this work we consider an extension MFcind of the Minimalist Foundation MF for predicative constructive mathematics with the addition of inductive and coinductive definitions suf…
Extending the extensional level of the Minimalist Foundation to axiomatic set theories
Samuele Maschio, Pietro Sabelli
We introduce extensions by rules of the extensional level of the Minimalist Foundation which turn out to be equivalent to constructive and classical axiomatic set theories.
Remarks on abstract structures of propositions and realizers
Samuele Maschio
We present here an abstract notion of structure consisting of propositions and realizers (which we call PR-structures) giving rise to set based contravariant functors taking values…
A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice
Maria Emilia Maietti, Samuele Maschio, Michael Rathjen
We present a Kleene realizability semantics for the intensional level of the Minimalist Foundation, for short mtt, extended with inductively generated formal topologies, Church's t…
Factorizing the Top-Loc adjunction through positive topologies
Francesco Ciraulo, Tatsuji Kawai, Samuele Maschio
We characterize the category of Sambin's positive topologies as a fibration over the category of locales Loc. The fibration is obtained by applying the Grothendieck construction to…
A predicative variant of Hyland's Effective Topos
Maria Emilia Maietti, Samuele Maschio
Here, we present a subcategory pEff of Hyland's Effective Topos Eff which can be considered a predicative variant of Eff itself. The construction of pEff is motivated by the desire…
Natural density and probability, constructively
Samuele Maschio
We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic v…
Topology as faithful communication through relations
Samuele Maschio, Giovanni Sambin
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts…
An extensional Kleene realizability semantics for the Minimalist Foundation
Maria Emilia Maietti, Samuele Maschio
We build a Kleene realizability semantics for the two-level Minimalist Foundation MF, ideated by Maietti and Sambin in 2005 and completed by Maietti in 2009. Thanks to this semanti…
Models of Intuitionistic Set Theory in Subtoposes of Nested Realizability Toposes
Samuele Maschio, Thomas Streicher
With every pca and subpca we associate the nested realizability topos within which we identify a class of s…
What is the real category of sets?
Samuele Maschio
Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands"…