Abstract
We discuss completions of basic algebras. We prove that the ideal completion of a basic algebra is also a basic algebra. It will be shown that basic algebras are not closed under MacNeille completions. By adding the join-infinite distributive law to basic algebras, we will show that these kind of basic algebras are closed under the closed ideal completion and moreover any other regular completions of these algebras are isomorphic to the closed ideal completion. As an application we establish an algebraic completeness theorem for a logic weaker than Visser’s basic predicate logic, BQL, a proper subsystem of intuitionistic predicate logic, IQL.
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Alizadeh, M. (2009). Completions of Basic Algebras. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_7
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DOI: https://doi.org/10.1007/978-3-642-02261-6_7
Publisher Name: Springer, Berlin, Heidelberg
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