Locally finite Jonsson conditional varieties and the conditional rational equivalence (Q1288129)

A notion of a locally finite Jonsson conditional variety is introduced. In the author's article [Algebra Logika 37, No. 4, 432-459 (1998; Zbl 0913.08008)], for two given conditional varieties, he studied the relationship between the isomorphism of the embedding categories of the varieties and the conditional rational equivalence of these varieties (there, the last term is translated as ``conditioned rational equivalence''); as an application, abstract invariants were described for the classes of conditionally rationally equivalent finite algebras and for the classes of similar finite algebras. In the article under review, abstract invariants are given for two locally finite Jonsson conditional varieties that are conditionally rationally equivalent.