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 -sound theories and of sentences that are -conservative over such a theory.
Topological Structure of Diagonalizable Algebras and Corresponding Logical Properties of Theories
D'AGOSTINO, Giovanna
1994-01-01
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 -sound theories and of sentences that are -conservative over such a theory.File | Dimensione | Formato | |
---|---|---|---|
euclid.ndjfl.1040408613.pdf
non disponibili
Tipologia:
Documento in Post-print
Licenza:
Non pubblico
Dimensione
92.5 kB
Formato
Adobe PDF
|
92.5 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.