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The Basic Picture on sets evaluated over an overlap algebra

ARGOMENTI: Convegni Dottorato

SEMINARIO DOTTORATO
Mmercoledi' 16 aprile 2008 alle ore 14:30, in aula 1BC/45
Paola TOTO (dottoranda in Matematica Pura - Universita` di Lecce) "The Basic Picture on sets evaluated over an overlap algebra"

-Abstract
In his forthcoming book, G. Sambin introduces a new topological theory, called "The Basic Picture". In this theory both the notion of topological space and its point-free version are generalized. The concept of overlap algebra is also introduced in order to put in algebraic form the properties needed to define the new topological structures.
In this seminar we shall give a tutorial introduction to our work, whose ultimate goal is to generalize such topological notions in the context of many-valued sets. In many-valued set theory sets are built by using propositions evaluated in an algebraic structure. To reach our goal a key point is to check whether the original algebrization of Sambin's topological notions can be considered also as the algebrization of their many-valued version. We prove that this is the case if and only if we take an overlap algebra as the underlying structure of truth values.

Rif. int. C. Marastoni, T. Vargiolu

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