4 papers
Equiconsistency of the Minimalist Foundation with its classical version
Maria Emilia Maietti, Pietro Sabelli
The Minimalist Foundation, for short MF, was conceived by the first author with G. Sambin in 2005, and fully formalized in 2009, as a common core among the most relevant constructi…
A topological reading of inductive and coinductive definitions in Dependent Type Theory
Pietro Sabelli
In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, in…
A topological counterpart of well-founded trees in dependent type theory
Maria Emilia Maietti, Pietro Sabelli
Within dependent type theory, we provide a topological counterpart of well-founded trees (for short, W-types) by using a proof-relevant version of the notion of inductively generat…
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.