The Lattice of Subquasivarieties of a Locally Finite Quasivariety

"This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout."-- Back cover Front Matter ....Pages I-XV Introduction and Background (Jennifer Hyndman, J. B. Nation)....Pages 1-10 Structure of Lattices of Subquasivarieties (Jennifer Hyndman, J. B. Nation)....Pages 11-36 Omission and Bases for Quasivarieties (Jennifer Hyndman, J. B. Nation)....Pages 37-47 Analyzing \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\) (Jennifer Hyndman, J. B. Nation)....Pages 49-64 Unary Algebras with 2-Element Range (Jennifer Hyndman, J. B. Nation)....Pages 65-102 1-Unary Algebras (Jennifer Hyndman, J. B. Nation)....Pages 103-120 Pure Unary Relational Structures (Jennifer Hyndman, J. B. Nation)....Pages 121-132 Problems (Jennifer Hyndman, J. B. Nation)....Pages 133-134 Back Matter ....Pages 135-162