3 citations · 4 across the 6 of their papers we have counts for
6 papers · 1 filter
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…
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 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…
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…
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"…