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VARIETIES OF POSITIVE MODAL ALGEBRAS AND STRUCTURAL COMPLETENESS

Published online by Cambridge University Press:  13 June 2019

TOMMASO MORASCHINI
TOMMASO MORASCHINI*
Affiliation:
Institute of Computer Science, Czech Academy of Science
*
*INSTITUTE OF COMPUTER SCIENCE CZECH ACADEMY OF SCIENCE PRAGUE, CZECH REPUBLIC E-mail: moraschini@cs.cas.cz
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Abstract

Positive modal algebras are the $$\left\langle { \wedge , \vee ,\diamondsuit ,\square,0,1} \right\rangle $$-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe the bottom part of the lattice of varieties of positive S4-algebras. Building on this, we characterize (passively, hereditarily) structurally complete varieties of positive K4-algebras.

Keywords

03G2703B4554F05positive modal logicmodal logicstructural completenessadmissible ruleabstract algebraic logicalgebraization of Gentzen systems
Type
Research Article
Information
The Review of Symbolic Logic , Volume 12 , Issue 3 , September 2019 , pp. 557 - 588
Copyright
Copyright © Association for Symbolic Logic 2019 

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