Brief
bio
Born in 1948, laurea in mathematics in 1971, professor since 1981,
first in Siena, later (since 1987) in Padua. Founder and first
president (1987-93) of the Italian Association of Logic and
Applications (AILA). Scientific coordinator since 1999 of five projects
financed by the italian government on Constructive Methods in
mathematics and computer science.
Coming from the school of mathematical logic of R. Magari in Siena, he
has been one of the founders of the modal logic of provability (the
fixed point theorem by de Jongh-Sambin, 1976).
In 1980-82 he took care of exposition for the only textbook by
Martin-Löf on his constructive type theory. In 1984 he started
formal topology (that is, topology as developed on the base of type
theory), which is by now widely known as one of the most fertile
branches of constructive mathematics. He has organized three Workshops
on Formal Topology (1997, 2002 and 2007).
In 1995 he discovered a logical duality between the notions of
open and closed in topology. This brought to positive topology, a
generalization of topology in which closed and open subsets are treated
on the same level. In particular, he introduced a primitive notion of
closed subset in pointfree topology, which starts an abstract
mathematical treatment of existential statements. His book on positive
topology will be published by Oxford U.P.
In 1995-96 he isolated basic logic, in which logical constants are
obtained through a reflection of metalanguage into object language and
which gives a conceptual and geometrical structure to the space of
logics.
He has always cultivated active interest in foundations of mathematics.
Since 1999 he has developed arguments in favour of a dynamic
constructivism. In 2005, in collaboration with M. E. Maietti, he
introduced a foundational theory according to such principles, called
minimalist.
