Implicative-groups vs Groups and Generalizations. Second Edition

This monograph is a comprehensive survey of several classes of algebras and, more generally, of first-order structures of great importance in algebra and logic, including groups, po-groups, l-groups, term-equivalent versions of such, and many of their generalisations. Many of these classes are very well-known, perhaps up to algebraic signature, while other ones are introduced here for the first time or constitute a development of previous work by the author.

This book stands out for its comprehensiveness and clarity. Not only are these algebras studied in great detail (with a lot of attention devoted to their arithmetical properties, something that is extremely beneficial to the reader, but also something that most textbooks lamentably skip), but also their mutual relationships are clarified by means of a number of term equivalence results in which the monograph abounds.

Francesco Paoli, Università degli Studi di Cagliari, Italy