Now in it's fourth edition, this classic work on logic presents the student with a clear, concise introduction to the subject of logic and its apllications. The first part of the book introduces the concepts and principles which make up the elements of logic, demonstrating that the concepts of logic are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The book goes on to show the applications of logic in mathematical theory building using concrete examples, drawing upon the concepts and principles presented in the first section. An introduction to the theory of real numbers is also presented. Exercises are included, designed to assist in the assimilation of the concepts and principles. Throughout the conceptual side or logic is stressed.Thoroughly revised by the author's son, the book remains a fundametal guide to modern mathematica logic and is a very important addition to this highly successful series.

Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject.

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. A thought-provoking introduction to the fundamentals and the perfect adjunct to courses in logic and the foundations of mathematics. Exercises appear throughout.

This revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Hermann & Cie, Paris, the onset of war delayed its release, with only proofs left as a record. The RAND Corporation''s interest in 1948 revived the project, resulting in a monograph focused on the systematic development of a decision method for elementary algebra and geometry, emphasizing its practical potential in creating a decision-making machine. Under the editorial guidance of Professor J.C.C. McKinsey, this work was refined with a new draft, clarifying key theoretical aspects and introducing simplifications to the development process. The current edition reproduces RAND''s publication with minor corrections, updated references, and supplementary notes that expand upon original theories, including fresh bibliographical insights. This title was originally published in 1951. This revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Herma

Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis''s systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.

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 papers and abstracts published during his lifetime, 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.

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.

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.

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.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Now in it's fourth edition, this classic work on logic presents the student with a clear, concise introduction to the subject of logic and its apllications. The first part of the book introduces the concepts and principles which make up the elements of logic, demonstrating that the concepts of logic are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The book goes on to show the applications of logic in mathematical theory building using concrete examples, drawing upon the concepts and principles presented in the first section. An introduction to the theory of real numbers is also presented. Exercises are included, designed to assist in the assimilation of the concepts and principles. Throughout the conceptual side or logic is stressed.Thoroughly revised by the author's son, the book remains a fundametal guide to modern mathematica logic and is a very important addition to this highly successful series.

Now in its fourth edition, this classic work clearly and concisely introduces the subject of logic and its applications. The first part of the book explains the basic concepts and principles which make up the elements of logic. The author demonstrates that these ideas are found in all branches of mathematics, and that logical laws are constantly applied in mathematical reasoning. The second part of the book shows the applications of logic in mathematical theory building with concrete examples that draw upon the concepts and principles presented in the first section. Numerous exercises and an introduction to the theory of real numbers are also presented. Students, teachers and general readers interested in logic and mathematics will find this book to be an invaluable introduction to the subject.

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. A thought-provoking introduction to the fundamentals and the perfect adjunct to courses in logic and the foundations of mathematics. Exercises appear throughout.

This revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Hermann & Cie, Paris, the onset of war delayed its release, with only proofs left as a record. The RAND Corporation''s interest in 1948 revived the project, resulting in a monograph focused on the systematic development of a decision method for elementary algebra and geometry, emphasizing its practical potential in creating a decision-making machine. Under the editorial guidance of Professor J.C.C. McKinsey, this work was refined with a new draft, clarifying key theoretical aspects and introducing simplifications to the development process. The current edition reproduces RAND''s publication with minor corrections, updated references, and supplementary notes that expand upon original theories, including fresh bibliographical insights. This title was originally published in 1951. This revised edition of A Decision Method for Elementary Algebra and Geometry presents the culmination of research begun in 1930, which laid foundational results in algebraic and geometric completeness. Originally intended for publication in 1939 by Herma

Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis''s systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.

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 papers and abstracts published during his lifetime, 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.

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.

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.

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.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.