A note on natural extensions in abstract algebraic logic (Q495839)

The paper analyses the existence of natural extensions of a logic for arbitrary new sets of variables (This concept was introduced by \textit{J. Czelakowski} [Protoalgebraic logics. Dordrecht: Kluwer Academic Publishers (2001; Zbl 0984.03002)]). The proof of the transfer principle and many results require the existence of natural extensions of the above kind. The authors show that the constructions of natural extensions known in the literature do not always work. They improve the foregoing constructions introducing a technical restriction that needs to be added to ensure the existence and the working of natural extensions.