Abstract
We study Basic algebra, the algebraic structure associated with basic propositional calculus, and some of its natural extensions. Among other things, we prove the amalgamation property for the class of Basic algebras, faithful Basic algebras and linear faithful Basic algebras. We also show that a faithful theory has the interpolation property if and only if its correspondence class of algebras has the amalgamation property.
Similar content being viewed by others
References
Aghaei M., Ardeshir M. (2001) Gentzen-style axiomatizations for some conservative extensions of basic propositional logic. Sudia Logica 68, 263–285
Alizadeh M., Ardeshir M. (2004) On the linear Lindenbaum algebra of basic propositional logic. Mathe. Log. Q. 50, 65–70
Ardeshir, M. Aspects of basic logic. PhD thesis, Department of Mathematics, Statistics and Computer Science, Marquette University (1995)
Ardeshir M., Ruitenburg W. (1998) Basic propositional calculus I. Math. Log. Q. 44, 317–343
Ardeshir M., Ruitenburg W. (2001) Basic propositional calculus II, interpolation. Arch. Math. Log. 40, 349–384
Celani S., Jansana R. (2005) Bounded distributive lattices with strict implication. Math. Log. Q. 51, 219–246
Maksimova L.L. (1979) Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-Boolian algebras. Algebra log. 16, 643–681
Suzuki Y., Wolter F., Zakharyaschev M. (1998) Speaking about transitive frames in propositional languages. J. Log. Lang. Inf. 7, 317–339
Tishkovskii D.E. (2001) Algebraic counterparts for some properties of superintuionistic predicate logics. Algebra Log. 40, 122–134
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alizadeh, M., Ardeshir, M. Amalgamation property for the class of basic algebras and some of its natural subclasses. Arch. Math. Logic 45, 913–930 (2006). https://doi.org/10.1007/s00153-006-0018-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-006-0018-y