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Fall 1994 Topological Structure of Diagonalizable Algebras and Corresponding Logical Properties of Theories
Giovanna D'Agostino
Notre Dame J. Formal Logic 35(4): 563-572 (Fall 1994). DOI: 10.1305/ndjfl/1040408613

Abstract

This paper studies the topological duality between diagonalizable algebras and bi-topological spaces. In particular, the correspondence between algebraic properties of a diagonalizable algebra and topological properties of its dual space is investigated. Since the main example of a diagonalizable algebra is the Lindenbaum algebra of an r.e. theory extending Peano Arithmetic, endowed with an operator defined by means of the provability predicate of the theory, this duality gives the possibility to study arithmetical properties of theories from a topological point of view. We find topological characterization of $\Sigma_1$-sound theories and of sentences that are $\Sigma_1$-conservative over such a theory.

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Giovanna D'Agostino. "Topological Structure of Diagonalizable Algebras and Corresponding Logical Properties of Theories." Notre Dame J. Formal Logic 35 (4) 563 - 572, Fall 1994. https://doi.org/10.1305/ndjfl/1040408613

Information

Published: Fall 1994
First available in Project Euclid: 20 December 2002

zbMATH: 0830.03035
MathSciNet: MR1334291
Digital Object Identifier: 10.1305/ndjfl/1040408613

Subjects:
Primary: 03G25
Secondary: 03F30, 06E25

Rights: Copyright © 1994 University of Notre Dame

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Vol.35 • No. 4 • Fall 1994
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