On finite models of regular identities
A regular identity is one where the same variables appear on both sides of \(=\). For each finite type \(\tau\) of algebras and each set A with a semilattice operation one can define a \(\tau\)-semilattice on A. \(\tau\)- semilattices are ``trivial'' models of regular identities. The authors give a finite set of regular identities \(\Sigma\) such that each finite model of \(\Sigma\) is a \(<2,2>\)-semilattice and such that \(\Sigma\) has a model which is not a \(<2,2>\)-semilattice. They also show that a single regular identity has a nontrivial finite model (not a \(\tau\)- semilattice).
scientific article; zbMATH DE number 4135925