Christopher C. Leary and Lars Kristiansen

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This book is written for upper division mathematics students with the aim of getting to and understanding the incompleteness theorems in a single semester. The authors outline two paths to this goal as described in the preface to the second edition:

This has allowed us to chart two paths to the incompleteness theorems, splitting after the material in Chapter 4. Readers of the first edition will find that the exposition in Chapters 5 and 6 follows a familiar route, although the material there has been pretty thoroughly reworked. It is also possible, if you choose, to move directly from Chapter 4 to Chapter 7 and see a development of computability theory that covers the Entschei- dungsproblem, Hilbert’s 10th Problem, and Gödel’s First Incompleteness Theorem.


  1. Structures and Languages
  2. Deductions
  3. Completeness and Compactness
  4. Incompleteness from Two Points of View
  5. Syntactic Incompleteness—Groundwork
  6. The Incompleteness Theorems
  7. Computability Theory
  8. Summing Up, Looking Ahead