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First Order Mathematical Logic

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First Order Mathematical Logic Cover

 

Synopses & Reviews

Publisher Comments:

"Attractive and well-written 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 well-written introduction to mathematical logic is aimed primarily at undergraduates with some background in college-level 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 smooth-running technique for proving theorem schemes is developed and exploited.

Chapter Three is devoted to first-order 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 one-semester 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 thought-provoking introduction to the logical underpinnings of mathematical theory.

"An excellent text." — Mathematical Reviews

Synopsis:

Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus.
Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.

Synopsis:

Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.


Synopsis:

Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order 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 Contents

1. 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

Product Details

ISBN:
9780486662695
Author:
Margaris, Angelo
Publisher:
Dover Publications
Author:
Mathematics
Subject:
General
Subject:
Mathematics
Subject:
Logic
Subject:
Logic, symbolic and mathematical
Subject:
First-order logic
Subject:
General Mathematics
Subject:
Mathematics-Logic and Philosophy
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19900331
Binding:
TRADE PAPER
Language:
English
Pages:
212
Dimensions:
8.5 x 5.38 in 0.55 lb

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Related Subjects

Humanities » Philosophy » Logic
Science and Mathematics » Biology » General
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First Order Mathematical Logic New Trade Paper
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$11.95 In Stock
Product details 212 pages Dover Publications - English 9780486662695 Reviews:
"Synopsis" by ,
Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus.
Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.

"Synopsis" by , Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.


"Synopsis" by ,
Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order 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.

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