Prime deductive systems and injective objects in the algebras of Łukasiewicz infinite-valued calculi
type: Item
instance of: scholarly article
title: Prime deductive systems and injective objects in the algebras of Łukasiewicz infinite-valued calculi
zbMATH Open document ID: 0786.03048
DOI: 10.1007/BF01212438
author: Daniel Gluschankof
published in: Algebra Universalis
publication date: 1993-04-01T00:00:00Z
review text: The author explores logical aspects of Wajsberg algebras. He proves that in any Wajsberg algebra, any proper implicative filter can be extended to a prime filter, and any proper deductive system can be extended to a maximal deductive system. He characterizes injective Wajsberg algebras as the retracts of powers of the algebra \(\mathbb{R}[0,1]\), and he proves that this characterization is equivalent to Sikorski Extension Theorem.
Mathematics Subject Classification ID: 03G20
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 06D30
zbMATH DE Number: 146929
zbMATH Keywords: logical aspects of Wajsberg algebras
zbMATH Keywords: implicative filter
zbMATH Keywords: prime filter
zbMATH Keywords: deductive system
zbMATH Keywords: injective Wajsberg algebras
zbMATH Keywords: Sikorski Extension Theorem
Wikidata QID: Q114234008
reviewed by: Manuel Abad
MaRDI profile type: Publication
cites work: Some propositions equivalent to the Sikorski Extension Theorem for Boolean algebras
cites work: Semisimple Algebras of Infinite Valued Logic and Bold Fuzzy Set Theory
cites work: Algebraic Analysis of Many Valued Logics
cites work: A New Proof of the Completeness of the Lukasiewicz Axioms
cites work: Representation of Łukasiewicz and Post algebras by continuous functions
cites work: Proper n-valued Lukasiewicz algebras as S-algebras of Lukasiewicz n- valued propositional calculi
cites work: Maximal Deductive Systems and Injective Objects in the Category of Hilbert Algebras
cites work: Birkhoff's representation theorem is equivalent to the axiom of choice
cites work: Q3863862
cites work: The Priestley duality for Wajsberg algebras
cites work: Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
cites work: Ordered Topological Spaces and the Representation of Distributive Lattices
cites work: W-algebras which are Boolean products of members of SR[1] and CW- algebras
cites work: Q5561935
description: scientific article; zbMATH DE number 146929