Contents -- From Author's Prefaces to Previous Editions -- Editor's Preface -- A Short Biographical Sketch of Alfred Tarski -- First Part. Elements of Logic. Deductive Method -- I: On the Use of Variables -- 1 Constants and variables -- 2 Expressions containing variables-sentential and designatory functions -- 3 Construction of sentences in which variables occur-universal and existential sentences -- 4 Universal and existential quantifiers -- free and bound variables -- 5 The importance of variables in mathematics -- Exercises -- II: On the Sentential Calculus -- 6 Logical constants -- the old logic and the new logic -- 7 Sentential calculus -- the negation of a sentence, the conjunction and the disjunction of sentences -- 8 Implications or conditional sentences -- implications in the material meaning -- 9 The use of implications in mathematics -- 10 Equivalence of sentences -- 11 The formulation of definitions and its rules -- 12 Laws of sentential calculus -- 13 The symbolism of sentential calculus -- compound sentential functions and truth tables -- 14 An application of laws of sentential calculus in inference -- 15 Rules of inference, complete proofs -- Exercises -- III: On the Theory of Identity -- 16 Logical concepts outside sentential calculus -- the concept of identity -- 17 Fundamental laws of the theory of identity -- 18 Identity of objects and identity of their designations -- the use of quotation marks -- 19 Equality in arithmetic and in geometry, and its relationship to logical identity -- 20 Numerical quantifiers -- Exercises -- IV: On the Theory of Classes -- 21 Classes and their elements -- 22 Classes and sentential functions with one free variable -- 23 The universal class and the null class -- 24 The fundamental relations among classes -- 25 Operations on classes.

26 Equinumerous classes, the cardinal number of a class, finite and infinite classes -- arithmetic as a part of logic -- Exercises -- V: On the Theory of Relations -- 27 Relations, their domains and counter-domains -- relations and sentential functions with two free variables -- 28 The algebra of relations -- 29 Several kinds of relations -- 30 Relations which are reflexive, symmetric, and transitive -- 31 Ordering relations -- examples of other relations -- 32 Many-one relations or functions -- 33 One-one relations or bijective functions, and one-to-one correspondences -- 34 Many-place relations -- functions of several variables and operations -- 35 The importance of logic for other sciences -- Exercises -- VI: On the Deductive Method -- 36 Fundamental constituents of a deductive theory-primitive and defined terms, axioms and theorems -- 37 Models and interpretations of a deductive theory -- 38 The law of deduction -- formal character of deductive sciences -- 39 Selection of axioms and primitive terms -- their independence -- 40 Formalization of definitions and proofs, formalized deductive theories -- 41 Consistency and completeness of a deductive theory -- the decision problem -- 42 The widened conception of the methodology of deductive sciences -- Exercises -- Second Part. Applications of Logic and Methodology in Constructing Mathematical Theories -- VII: Construction of a Mathematical Theory: Laws of Order for Numbers -- 43 The primitive terms of the theory to be constructed -- the axioms concerning the fundamental relations among numbers -- 44 The laws of irreflexivity for the fundamental relations -- indirect proofs -- 45 Further theorems on the fundamental relations -- 46 Other relations among numbers -- Exercises -- VIII: Construction of a Mathematical Theory: Laws of Addition and Subtraction -- 47 The axioms concerning addition.

general properties of operations, the concept of a group and the concept of an Abelian group -- 48 Commutative and associative laws for larger numbers of summands -- 49 The laws of monotonicity for addition and their converses -- 50 Closed systems of sentences -- 51 A few consequences of the laws of monotonicity -- 52 The definition of subtraction -- inverse operations -- 53 Definitions whose definiendum contains the identity sign -- 54 Theorems on subtraction -- Exercises -- IX: Methodological Considerations on the Constructed Theory -- 55 Elimination of superfluous axioms from the original axiom system -- 56 Independence of the axioms of the reduced system -- 57 Elimination of a superfluous primitive term and the subsequent simplification of the axiom system -- the concept of an ordered Abelian group -- 58 Further simplification of the axiom system -- possible transformations of the system of primitive terms -- 59 The problem of consistency of the constructed theory -- 60 The problem of completeness of the constructed theory -- Exercises -- X: Extension of the Constructed Theory: Foundations of Arithmetic of Real Numbers -- 61 The first axiom system for the arithmetic of real numbers -- 62 Closer characterization of the first axiom system -- its methodological advantages and didactic disadvantages -- 63 The second axiom system for the arithmetic of real numbers -- 64 Closer characterization of the second axiom system -- the concept of a field and that of an ordered field -- 65 Equipollence of the two axiom systems -- methodological disadvantages and didactic advantages of the second system -- Exercises -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.