Kira Adaricheva,Jennifer Hyndman,J. B. Nation,Joy N. Nishida
A Primer of Subquasivariety Lattices
A Primer of Subquasivariety Lattices
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- More about A Primer of Subquasivariety Lattices
The book addresses Birkhoff and Mal cev s problem of describing subquasivariety lattices, representing them as lattices of closed algebraic subsets of a lattice with operators, and applying this approach to completely distributive lattices with a dually compact least element. It provides examples and open problems to investigate classes of lattices that can be represented as subquasivariety lattices.
Format: Paperback / softback
Length: 290 pages
Publication date: 20 August 2023
Publisher: Springer Nature Switzerland AG
Birkhoff and MacNeille's problem of describing subquasivariety lattices is addressed in this book. It starts by establishing the foundations of atomic and implicational theories in languages that may or may not include equality. Subquasivariety lattices are then represented as lattices of closed algebraic subsets of a lattice with operators, which leads to new restrictions on the equaclosure operator. As an application of this new approach, it is demonstrated that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book includes numerous examples to illustrate these principles, as well as open problems. Ultimately, this new approach provides readers with a set of tools to explore classes of lattices that can be represented as subquasivariety lattices.
Dimension: 235 x 155 (mm)
ISBN-13: 9783030980900
Edition number: 1st ed. 2022
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