For more detail on the topics briefly introduced here, the reader can be referred to: S. Burris, H. P Sankappanavar  for universal algebra, lattice theory, first order logic and decidability; S. Burris, R. McKenzie  for several theorems quoted here; and D. Hobby, R. McKenzie  for a detailed development of tame congruence theory, including many results that will be applied here. The introductory chapters in Burris and McKenzie contain an introduction to decidability, interpretations, discriminator varieties and affine varieties that complements what we write here. The proofs in Burris and McKenzie relied on several results about commutators in congruence-modular varieties that had not appeared in print at that time. The reader was referred for these results to a preprint by R. Freese and R. McKenzie titled . That paper has now been published (much expanded) as Freese, McKenzie .
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