A
trivial algebra contains just one element. A
quasivariety is a class
K of algebras with a specified
signature satisfying any of the following equivalent conditions: •
K is a
pseudoelementary class closed under
subalgebras and
direct products. •
K is the class of all
models of a set of
quasi-identities, that is, implications of the form s_1 \approx t_1 \land \ldots \land s_n \approx t_n \rightarrow s \approx t, where s, s_1, \ldots, s_n,t, t_1, \ldots, t_n are
terms built up from variables using the operation symbols of the specified signature. •
K contains a trivial algebra and is closed under
isomorphisms, subalgebras, and
reduced products. •
K contains a trivial algebra and is closed under isomorphisms, subalgebras, direct products, and
ultraproducts. == Examples ==