Collected Papers: Volume 3: 1945-1957

Alfred Tarski was one of the two giants of the twentieth-century development of logic, along with Kurt Goedel. The four volumes of this collection contain all of Tarski's published papers and abstracts, as well as a comprehensive bibliography. Here will be found many of the works, spanning the period 1921 through 1979, which are the bedrock of contemporary areas of logic, whether in mathematics or philosophy. These areas include the theory of truth in formalized languages, decision methods and undecidable theories, foundations of geometry, set theory, and model theory, algebraic logic, and universal algebra. Ideale in vollstndigen Mengenkrpern, II.- On closed elements in closure algebras (with J.C. C. McKinsey).- A remark on functionally free algebras.- Direct decompositions of finite algebraic systems (with B. Jnsson).- Some theorems about the sentential calculi of Lewis and Heyting (with J. C. C. McKinsey).- A problem concerning the notion of definability.- Axiomatic and algebraic aspects of two theorems on sums of cardinals.- Measures in Boolean algebras (with A. Horn).- Cancellation laws in the arithmetic of cardinals.- Distributive and modular laws in the arithmetic of relation algebras (with L. H. Chin).- A decision method for elementary algebra and geometry (prepared for publication with the assistance of J. C. C. McKinsey).- Boolean algebras with operators, Part I (with B. Jnsson).- Boolean algebras with operators, Part II (with B. Jnsson).- Some notions and methods on the borderline of algebra and metamathematics.- Mutual interpretability of some essentially undecidable theories (with W. Szmielew).- On algebras whose factor algebras are Boolean (with J. M. G. Fell).- Theorems on the existence of successors of cardinals, and the axiom of choice.- Contributions to the theory of models, I.- Contributions to the theory of models, II.- Contributions to the theory of models, III.- A lattice-theoretical fixpoint theorem and its applications.- The fundamental ideas of pansomatism (English translation of the article Zasadnicze mysli pansomatyzmu by T. Kotarbinski; translated by A. Tarski and D. Rynin).- Equationally complete rings and relation algebras.- Equilaterality as the only primitive notion of Euclidean geometry (with E. W. Beth).- A general theorem concerning primitive notions of Euclidean geometry.- Higher degrees of distributivity and completeness in Boolean algebras (with E. C. Smith, Jr.).- Arithmetical extensions of relational systems (with R. L. Vaught).- Remarks on direct products of commutative semigroups.