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A Course in Universal Algebra
by Stanley N. Burris and H.P. Sankappanavar
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Universal algebra has enjoyed an especially explosive growth in the last twenty Years, and students entering the subject now will find a bewildering amount of material to digest. Chapter I have a brief but important introduction to lattices, and to the close connection between complete lattices and closure operators. In particular, all necessary for the consecutive study of agreement lattices is included. The final chapter gives the reader a gentle introduction to some basic concepts, tools, and results of model theory. In exact, we use the ultra product construction to derive the compactness theorem and to prove fundamental preservation theorems. Principal congruence formulas are a favorite model-theoretic tool of universal algebraists, and we use them in the study of the sizes of sub directly irreducible algebras.
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