No abstract

A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references.Keywords: Algebraic logic, finitely algebraizable logic, abstract algebraic logic, quasivariety.Our paper A Survey of Abstract Algebraic Logic [Su] presents, among other notions, the concept of algebraizability of a logical system. This concept was introduced by W. Blok and D. Pigozzi in [23]. In their monograph only finitary logics are considered, and their algebraic counterparts are restricted to quasivarieties; as a consequence, the interpretations involved in the original notion of an algebraizable logic are assumed to be finite. Later on all these finiteness restrictions have been removed in the works of other scholars such as Herrmann, Dellunde or Czelakowski. Accordingly the term "algebraizable" in the literature has come to be used for a more general notion, and some adjectives qualifying "algebraizable" are now in common usage to refer to several stricter versions, among them one incorporating the finitary original character. Section 3.3 of [Su] introduces the notion of algebraizable logic by describing Blok and Pigozzi's original approach, but using the new terminology and without explicitly assuming that the logics are finitary, in a way that is not consistent with later usage in the same paper. Moreover, we have detected a linguistic confusion when cross-referencing two conditions that share the same label. Since the Survey intends to give compact and reliable references to notions and results that were scattered in the literature or were simply part of the folklore of the field at the time of publication, we believe it may be useful to publish some precisions.The context where the algebraizability of logics is discussed in [Su] is the following. We reproduce here the main definitions and notations involved, as they appear in pages 38-39 of [Su]:

No abstract

No abstract

No abstract

No abstract

No abstract

No abstract