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First Order Mathematical Logicby Angelo Margaris
Synopses & ReviewsPublisher Comments:"Attractive and wellwritten introduction." — Journal of Symbolic Logic
The logic that mathematicians use to prove their theorems is itself a part of mathematics, in the same way that algebra, analysis, and geometry are parts of mathematics. This attractive and wellwritten introduction to mathematical logic is aimed primarily at undergraduates with some background in collegelevel mathematics; however, little or no acquaintance with abstract mathematics is needed. Divided into three chapters, the book begins with a brief encounter of naïve set theory and logic for the beginner, and proceeds to set forth in elementary and intuitive form the themes developed formally and in detail later. In Chapter Two, the predicate calculus is developed as a formal axiomatic theory. The statement calculus, presented as a part of the predicate calculus, is treated in detail from the axiom schemes through the deduction theorem to the completeness theorem. Then the full predicate calculus is taken up again, and a smoothrunning technique for proving theorem schemes is developed and exploited. Chapter Three is devoted to firstorder theories, i.e., mathematical theories for which the predicate calculus serves as a base. Axioms and short developments are given for number theory and a few algebraic theories. Then the metamathematical notions of consistency, completeness, independence, categoricity, and decidability are discussed, The predicate calculus is proved to be complete. The book concludes with an outline of Godel's incompleteness theorem. Ideal for a onesemester course, this concise text offers more detail and mathematically relevant examples than those available in elementary books on logic. Carefully chosen exercises, with selected answers, help students test their grasp of the material. For any student of mathematics, logic, or the interrelationship of the two, this book represents a thoughtprovoking introduction to the logical underpinnings of mathematical theory. "An excellent text." — Mathematical Reviews Synopsis:Wellwritten undergraduatelevel introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers firstorder theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.Synopsis:Wellwritten undergraduatelevel introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers firstorder theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.
Synopsis:Wellwritten undergraduatelevel introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Firstorder theories are discussed in some detail, with special emphasis on number theory. After a discussion of truth and models, the completeness theorem is proved. ". . . an excellent text." — Mathematical Reviews. Exercises. Bibliography. Table of Contents1. Introduction
1. Rules of Inference 2. Set Theory 3. Axiomatic Theories 4. Predicates and Quantifiers 5. Statement Connectives 6. The Interpretation of Predicates and Quantifiers 7. The Predicate Calculus and First Order Theories 8. The Omission of Parentheses 9. Substitution of a Term for a Variable 10. Removing and Inserting Quantifiers 11. Denials 2. The Predicate Calculus 12. Formulation 13. The Statement Calculus 14. The Deudction Theorem 15. The Completeness Theorem for the Statement Calculus 16. Applications of the Completeness Theorem for the Statement Calculus 17. Quantifiers 18. Equivalence and Replacement 19. Theorem Schemes 20. Normal Forms 21. Equality 3. First Order Theories 22. Definition and Examples 23. Deduction 24. Number Theory 25. Consistency and Completeness 26. Truth 27. The Completeness Theorem 28. Independence 29. Completeness and Categoricity 30. Decidability 31. Gödel's Theorem Notes; References; Addendum; Index of Symbols; Subject Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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