Constructive version of Boolean algebra

The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds classically to that of map preserving arbitrary joins; we provid...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Ciraulo, Francesco, Maietti, Maria Emilia, Toto, Paola
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.03.2012
Subjects
Algebra
Boolean algebra
Mathematics - Logic
Topology
Online AccessGet full text

Cover

More Information
Summary:The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds classically to that of map preserving arbitrary joins; we provide a description of atomic set-based overlap algebras in the language of formal topology, thus giving a predicative characterization of discrete locales; we show that the power-collection of a set is the free overlap algebra join-generated from the set. Then, we generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins.
ISSN:2331-8422
DOI:10.48550/arxiv.1203.4997