FINITE REPLACEMENT AND FINITE HILBERT‐STYLE AXIOMATIZABILITY
Burghard Herrmann, Wolfgang Rautenberg · Mathematical logic quarterly · 1992
Abstract We define a property for varieties V, thef.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 thef.r.p.Essentially this implies finite axiomatizability of a 2‐valued logic inany finitelanguage.