Nonstandard characterization of pseudovarieties
A pseudovariety of algebras of a given type is understood as a class of finite algebras of that type which is closed under subalgebras, homomorphic images, and finite direct products. The author uses the main principles of nonstandard analysis to provide a new approach to pseudovarieties and the nonstandard identities that define them. The main results cannot be described here, as too many new concepts have to be defined. It turns out that one can consider nonstandard varieties of algebras as counterparts of pseudovarieties. Also, a nonstandard interpretation of implicit operations is given.
scientific article; zbMATH DE number 780796