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Friendly Introduction to Mathematical Logic

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Friendly Introduction to Mathematical Logic

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.

Mathematical Logic and ProofMathematics
Author
Christopher Leary & Lars Kristiansen
Publisher
SUNY Geneseo & University of Oslo
Source
LibreTexts
License
CC BY-NC-SA
Language
EN
Category
Basic Sciences
Read online Download PDF (open licence)
Contents· 56 sections
  1. 01: Structures and Languages
  2. 1.01: Summing Up Looking Ahead
  3. 1.02: Naively
  4. 1.03: Languages
  5. 1.04: Terms and Formulas
  6. 1.05: Induction
  7. 1.06: Sentences
  8. 1.07: Structures
  9. 1.08: Truth in a Structure
  10. 1.09: Substitutions and Substitutability
  11. 1.10: Logical Implication
  12. 02: Deductions
  13. 2.01: Naively
  14. 2.02: Deductions
  15. 2.03: The Logical Axioms
  16. 2.04: Rules of Inference
  17. 2.05: Soundness
  18. 2.06: Two Technical Lemmas
  19. 2.07: Properties of Our Deductive System
  20. 2.08: Nonlogical Axioms
  21. 2.09: Summing Up Looking Ahead
  22. 03: Completeness and Compactness
  23. 3.01: Naively
  24. 3.02: Completeness
  25. 3.03: Compactness
  26. 3.04: Substructures and the Lowenheim-Skolem Theorems
  27. 3.05: Summing Up Looking Ahead
  28. 04: Incompleteness From Two Points of View
  29. 4.01: Introduction to Incompleteness
  30. 4.02: Complexity of Formulas
  31. 4.03: The Roadmap to Incompleteness
  32. 4.04: An Alternate Route
  33. 4.05: How to Code a Sequence of Numbers
  34. 4.06: An Old Friend
  35. 4.07: Summing Up Looking Ahead
  36. 05: Syntactic Incompleteness Groundwork
  37. 5.01: Introduction
  38. 5.02: The Language the Structure and the Axioms of N
  39. 5.03: Representable Sets and Functions
  40. 5.04: Representable Functions and Computer Programs
  41. 5.05: Coding - Naively
  42. 5.06: Coding Is Representable
  43. 5.07: Godel Numbering
  44. 5.08: Godel Numbers and N
  45. 5.09: NUM and SUB Are Representable
  46. 5.10: Definitions by Recursion are Representable
  47. 5.11: The Collection of Axioms Is Representable
  48. 5.12: Coding Deductions
  49. 5.13: Summing Up Looking Ahead
  50. 06: The Incompleteness Theorems
  51. 6.01: Introduction to the Incompleteness Theorems
  52. 6.02: The Self-Reference Lemma
  53. 6.03: Section 3-
  54. 6.04: Section 4-
  55. 6.05: Section 5-
  56. 6.06: Section 6-