Publisher’s description: The publication of H. Rasiowa and R. Sikorski’s [The mathematics of metamathematics. Warszawa: Panstwowe Wydawnictwo Naukowe (1963; Zbl 0122.24311)], H. Rasiowa’s [An algebraic approach to non-classical logics. Amsterdam- London: North-Holland Publishing Company; New York: American Elsevier Publishing Company, Inc. (1974; Zbl 0299.02069)], and R. Wójcicki’s [Theory of logical calculi. Basic theory of consequence operations. Dordrecht etc.: Kluwer Academic Publishers (1988; Zbl 0682.03001)] created a niche in the field of mathematical and philosophical logic. This in-depth study of the concept of a consequence relation, culminating in the concept of a Lindenbaum-Tarski algebra, fills this niche. Citkin and Muravitsky consider the problem of obtaining confirmation that a statement is a consequence of a set of statements as prerequisites, on the one hand, and the problem of demonstrating that such confirmation does not exist in the structure under consideration, on the other hand. For the second part of this problem, the concept of the Lindenbaum-Tarski algebra plays a key role, which becomes even more important when the considered consequence relation is placed in the context of decidability. This role is traced in the book for various formal objective languages.
The work also includes helpful exercises to aid the reader’s assimilation of the book’s material. Intended for advanced undergraduate and graduate students in mathematics and philosophy, this book can be used to teach special courses in logic with an emphasis on algebraic methods, for self-study, and also as a reference work.