A characterization of decidable locally finite varieties. (English) Zbl 0760.08003
Algebra, Proc. Int. Conf. Memory A. I. Mal’cev, Novosibirsk/USSR 1989, Contemp. Math. 131, Pt. 3, 169-185 (1992).
Summary: [For the entire collection see Zbl 0745.00034.]
We describe the structure of those locally finite varieties whose first- order theory is decidable. A variety is a class of universal algebras defined by a set of equations. Such a class is said to be locally finite if every finitely generated member of the class is finite. It turns out that in order for such a variety to have a decidale theory it must decompose into the varietal product of three special kinds of varieties; a strongly Abelian variety; an affine variety; and a discriminator variety.
We describe the structure of those locally finite varieties whose first- order theory is decidable. A variety is a class of universal algebras defined by a set of equations. Such a class is said to be locally finite if every finitely generated member of the class is finite. It turns out that in order for such a variety to have a decidale theory it must decompose into the varietal product of three special kinds of varieties; a strongly Abelian variety; an affine variety; and a discriminator variety.
MSC:
| 08B05 | Equational logic, Mal’tsev conditions |
| 08B25 | Products, amalgamated products, and other kinds of limits and colimits |
| 03B25 | Decidability of theories and sets of sentences |
