Friendly Introduction to Mathematical Logic

by Christopher Leary & Lars Kristiansen

Read here Read at LibreTextsPDF

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.

Description from LibreTexts.

Publisher
SUNY Geneseo & University of Oslo
Subjects
Mathematics, Mathematical Logic and Proof
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Teens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Structures and Languages
  7. 1.1: Summing Up, Looking Ahead
  8. 1.2: Naïvely
  9. 1.3: Languages
  10. 1.4: Terms and Formulas
  11. 1.5: Induction
  12. 1.6: Sentences
  13. 1.7: Structures
  14. 1.8: Truth in a Structure
  15. 1.9: Substitutions and Substitutability
  16. 1.10: Logical Implication
  17. 2: Deductions
  18. 2.1: Naïvely
  19. 2.2: Deductions
  20. 2.3: The Logical Axioms
  21. 2.4: Rules of Inference
  22. 2.5: Soundness
  23. 2.6: Two Technical Lemmas
  24. 2.7: Properties of Our Deductive System
  25. 2.8: Nonlogical Axioms
  26. 2.9: Summing Up, Looking Ahead
  27. 3: Completeness and Compactness
  28. 3.1: Naïvely
  29. 3.2: Completeness
  30. 3.3: Compactness
  31. 3.4: Substructures and the Löwenheim-Skolem Theorems
  32. 3.5: Summing Up, Looking Ahead
  33. 4: Incompleteness From Two Points of View
  34. 4.1: Introduction to Incompleteness
  35. 4.2: Complexity of Formulas
  36. 4.3: The Roadmap to Incompleteness
  37. 4.4: An Alternate Route
  38. 4.5: How to Code a Sequence of Numbers
  39. 4.6: An Old Friend
  40. 4.7: Summing Up, Looking Ahead
  41. 5: Syntactic Incompleteness - Groundwork
  42. 5.1: Introduction
  43. 5.2: The Language, the Structure, and the Axioms of N
  44. 5.3: Representable Sets and Functions
  45. 5.4: Representable Functions and Computer Programs
  46. 5.5: Coding - Naïvely
  47. 5.6: Coding Is Representable
  48. 5.7: Gödel Numbering
  49. 5.8: Gödel Numbers and N
  50. 5.9: NUM and SUB Are Representable
  51. 5.10: Definitions by Recursion are Representable
  52. 5.11: The Collection of Axioms Is Representable
  53. 5.12: Coding Deductions
  54. 5.13: Summing Up, Looking Ahead
  55. 6: The Incompleteness Theorems
  56. 6.1: Introduction to the Incompleteness Theorems
  57. 6.2: The Self-Reference Lemma
  58. 6.3: Section 3-
  59. 6.4: Section 4-
  60. 6.5: Section 5-
  61. 6.6: Section 6-
  62. Back Matter
  63. Index
  64. Glossary
  65. Detailed Licensing