Abstract
This paper belongs to our series of works on algebraic geometry over arbitrary algebraic structures. In this one, there will be investigated seven equivalences (namely: geometric, universal geometric, quasi-equational, universal, elementary, and combinations thereof) in specific classes of algebraic structures (equationally Noetherian, qω-compact, uω-compact, equational domains, equational co-domains, etc.). The main questions are the following: (1) Which equivalences coincide inside a given class K, which do not? (2) With respect to which equivalences a given class K is invariant, with respect to which it is not?
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