The Lattice Of Interpretability Types Of Varieties

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The Lattice of Interpretability Types of Varieties

Author: Octavio Carlos García
language: en
Publisher: American Mathematical Soc.
Release Date: 1984
We investigate the lattice, invented by W. D. Neumann in 1974, formed by the class of all varieties under the quasi-ordering "[script]V is interpretable in [script]W." The lattice is found to be non-modular and a proper class. Various familiar varieties are found to be [logical conjunction symbol {up arrow}]-irreducible (or prime) and various filters (especially Mal'tsev classes) are found to be indecomposable (or prime). Many familiar varieties are found to be inequivalent in the lattice, using a new technique of SIN algebras. Seven figures are included which document the known relationships between some sixty known or easily describable varieties and varietal families.
The Lattice of Interpretability Types of Varieties

Author: Octavio Carlos García
language: en
Publisher: Amer Mathematical Society
Release Date: 2005-10-06