Bounded and well-placed theories in the lattice of equational theories
Let T be a fully invariant congruence relation on a term algebra \({\mathfrak A}\) of similarity type \(\rho\), i.e. an equational theory of type \(\rho\). The theory T is said to be bounded iff the number of orbits of \({\mathfrak A}/T\) under the (induced) action of Aut(\({\mathfrak A})\) is finite. The class of bounded theories and some of its subclasses, called well-placed, are studied. In particular, it turned out that in the case of a type with only one operation symbol and without constant symbol, the theory T is bounded iff it is an extension of a well-placed theory. Another result of the paper says that if \(\rho\) is the same as above, then, under the additional assumption that T is absorptive, i.e. (x,t)\(\in T\) for some term t which is not a variable, the theory T is bounded iff it is well- placed.
scientific article; zbMATH DE number 4139824