Logic

Book

• Download the book here: Logic (PDF).

Chapters

Part I — True/False Logic

• True/False Logic
• Proofs
• Which Connectives Are Useful?
• Compactness Theorem

Part II — First-Order Logic

• First-Order Logic
• Variables and Structures
• Satisfaction
• Proofs
• Soundness Theorem
• Completeness Theorem
• Proof of the Completeness Theorem

Part III — Gödel's Incompleteness Theorems

• An Overview of Gödel's Incompleteness Theorems
• Peano Arithmetic
• Gödel Coding
• Primitive Recursive Functions
• Representable Functions
• Diagonalization
• Proof of the Incompleteness Theorem
• The Second Incompleteness Theorem

Source Files

The source files are available in the Logic GitHub repository.

This book was translated by ChatGPT 5.6 from the original French version.

Errors

Please report any errors you find, whether logical, mathematical, or typographical.

Author

Arnaud Bodin

I would like to thank Stéphanie Bodin and Michel Bodin for proofreading the book.

This book is distributed under the Creative Commons BY-NC-SA 4.0 license.