"** new foundations must give new math**"

from

by Giovanni Sambin, Oxford University Press, forthcoming

Registration

To register send an e-mail to maietti @ math.unipd.it

Registration fee: 40 euros

(to be paid at arrival).

Under the patronage of

Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, Italy

University of Padova, Italy

AILA (Italian Association of Logic and Applications), whose first president was Giovanni Sambin (from 1987 to 1994).

Abstracts »
Toto

**Paola Toto**

Lecce

**Many-valued overlap algebras**

(j.w.w. **Maria Emilia Maietti** and **Giovanni
Sambin**)

In his forthcoming book Sambin introduces a new topological theory,
called "The Basic Picture", that generalizes the notion of topological
space and in turn its point-free version. He also introduces the notion
of overlap algebra to give a purely algebraic presentation of such
concepts.

The ultimate goal of our work is to generalize such topological notions
in the context of many-valued sets and to test whether the original
algebrization of Sambinâ€™s topological notions can be considered also
the algebrization of their many-valued version.

To include the many-valued power collection of a set as an example
of overlap algebra, we need to work in the many-valued
set theory whose structure of truth values is an overlap algebra itself.

After defining an evaluated set-based
overlap algebra, we prove that the evaluated power collection functor
is full and faithful and also dense over evaluated atomic overlap algebras,
as proved by Sambin in his book.