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Completed in 1983, this work culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. Written in collaboration with Steven Givant, the book appeals to a very broad audience, and requires only a familiarity with first-order logic. It is of great interest to logicians and mathematicians interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, algebraic logic, or the methodology of the deductive sciences, and to computer scientists interested in developing very simple computer languages rich enough for mathematical and scientific applications.

Mathematical logic --- Set theory --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Mathematics --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Set theory. --- Logic, Symbolic and mathematical. --- Théorie des ensembles. --- Logique symbolique et mathématique. --- Axiomatische Mengenlehre. --- Mathematische Logik. --- Mengenlehre. --- Verzamelingen (wiskunde). --- Teoria Dos Conjuntos. --- Théorie des ensembles

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This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, Introduction to Relation Algebras (Springer, 2017).

Relation algebras. --- Algebraic logic. --- Algebra of relations --- Algebras, Relation --- Relational algebras --- Relations, Algebra of --- Mathematics. --- Algebra. --- Mathematical logic. --- Mathematical Logic and Foundations. --- Logic, Symbolic and mathematical --- Algebraic logic --- Logic, Symbolic and mathematical. --- Mathematics --- Mathematical analysis --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism