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On Löb algebras
Author(s) -
Alizadeh Majid,
Ardeshir Mohammad
Publication year - 2006
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200510016
Subject(s) - variety (cybernetics) , mathematics , propositional calculus , gödel's completeness theorem , completeness (order theory) , pure mathematics , algebra over a field , discrete mathematics , mathematical analysis , statistics
We study the variety of Löb algebras , the algebraic structures associated with formal propositional calculus. Among other things, we prove a completeness theorem for formal propositional logic with respect to the variety of Löb algebras. We show that the variety of Löb algebras has the weak amalgamation property. Some interesting subclasses of the variety of Löb algebras, e.g. linear, faithful and strongly linear Löb algebras are introduced. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)