The Jacobson radical of a propositional theory

Fellin, Giulio; Schuster, Peter und Wessel, Daniel (2022): The Jacobson radical of a propositional theory. In: Bulletin of Symbolic Logic, Bd. 28, Nr. 2, PII S1079898621000664: S. 163-181

Abstract

Alongside the analogy between maximal ideals and complete theories, the Jacobson radical carries over from ideals of commutative rings to theories of propositional calculi. This prompts a variant of Lindenbaum's Lemma that relates classical validity and intuitionistic provability, and the syntactical counterpart of which is Glivenko's Theorem. The Jacobson radical in fact turns out to coincide with the classical deductive closure. As a by-product we obtain a possible interpretation in logic of the axioms-as-rules conservation criterion for a multi-conclusion Scott-style entailment relation over a single-conclusion one.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 1079-8986
• Sprache: Englisch