Implicit expressibility in two-valued logic and cryptoisomorphisms of two-element algebras (Q1380266)

The author presents a summary of his results (11 theorems) on the problem of implicit expressibility in two-valued logic, according to \textit{A. V. Kuznetsov} [Logical inference (Logicheskij vyvod), Proc. All-Union Symp. Theory of Logical Inference, Moscow March 1974, 5-33 (1979; Zbl 0605.03001)]. He establishes the equivalence of implicit expressibilty, implicit reducibility, and parametric reducibility and investigates the corresponding notions of implicit closedness and completeness. In conclusion, a classification of algebras on a two-element set is given, up to crypto-isomorphism in the sense of G. Birkhoff. Proofs are not included.