| Abstract: | We define a property for varieties V, the f.r.p. (finite replacement property). If it applies to a finitely based V then V is strongly finitely based in the sense of 14], see Theorem 2. Moreover, we obtain finite axiomatizability results for certain propositional logics associated with V, in its generality comparable to well-known finite base results from equational logic. Theorem 3 states that each variety generated by a 2-element algebra has the f.r.p. Essentially this implies finite axiomatizability of a 2-valued logic in any finite language. |
