Elsevier S & T

A Mathematical Introduction to Logic

Enderton, Herbert; Enderton, Herbert B.

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Table of contents
  • Contentsvii
  • Prefaceix
  • Introductionxi
  • Chapter Zero. Useful Facts about Sets1
  • Chapter One. Sentential Logic11
  • 1.0 Informal Remarks on Formal Languages11
  • 1.1 The Language of Sentential Logic13
  • 1.2 Truth Assignments20
  • 1.3 A Parsing Algorithm29
  • 1.4 Induction and Recursion34
  • 1.5 Sentential Connectives45
  • 1.6 Switching Circuits54
  • 1.7 Compactness and Effectiveness59
  • Chapter Two. First-Order Logic67
  • 2.0 Preliminary Remarks67
  • 2.1 First-Order Languages69
  • 2.2 Truth and Models80
  • 2.3 A Parsing Algorithm105
  • 2.4 A Deductive Calculus109
  • 2.5 Soundness and Completeness Theorems131
  • 2.6 Models of Theories147
  • 2.7 Interpretations Between Theories164
  • 2.8 Nonstandard Analysis173
  • Chapter Three. Undecidability182
  • 3.0 Number Theory182
  • 3.1 Natural Numbers with Successor187
  • 3.2 Other Reducts of Number Theory193
  • 3.3 A Subtheory of Number Theory202
  • 3.4 Arithmetization of Syntax224
  • 3.5 Incompleteness and Undecidability234
  • 3.6 Recursive Functions247
  • 3.7 Second Incompleteness Theorem266
  • 3.8 Representing Exponentiation276
  • Chapter Four. Second-Order Logic282
  • 4.1 Second-Order Languages282
  • 4.2 Skolem Functions287
  • 4.3 Many-Sorted Logic295
  • 4.4 General Structures299
  • Suggestions For Further Reading307
  • List of Symbols309
  • Index311
Book details
  • Vendor Elsevier S & T
  • SKU 9780122384523
  • ISBN-13 9780080496467
  • Author Enderton, Herbert; Enderton, Herbert B.
  • Edition 2nd
  • Category Mathematics
  • Subject Logic

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Description eBook delivery & access Reviews
A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional coverage of introductory material such as sets.

* Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses.
* Reduced mathematical rigour to fit the needs of undergraduate students