# Mathematical Logic

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Category: Mathematics
Slides: 32
Updated: 2026-05-15T22:18:40.380Z
Tags: mathematics, mathematical, logic

## Summary

The mathematical study of mathematical reasoning. Key sections include: Mathematical Logic.; What logic is.; Aristotle's syllogisms.; The algebra of logic.; Begriffsschrift.; Russell's paradox.; Principia Mathematica.; A finitary foundation.; Incompleteness.; The first incompleteness theorem..

## Slide Outline

1. Mathematical Logic.
2. What logic is.
3. Aristotle's syllogisms.
4. The algebra of logic.
5. Begriffsschrift.
6. Russell's paradox.
7. Principia Mathematica.
8. A finitary foundation.
9. Incompleteness.
10. The first incompleteness theorem.
11. The second incompleteness theorem.
12. What Gödel did not prove.
13. Tarski and truth.
14. The Turing machine.
15. The halting problem.
16. Church's lambda calculus.
17. The Church-Turing thesis.
18. Recursion theory.
19. Set theory and the ZFC axioms.
20. The continuum hypothesis.
21. The technique of forcing.
22. Large cardinal axioms.
23. Model theory.
24. Proof theory.
25. Type theory and constructive logic.
26. Modal logic.
27. Coq, Lean, and machine-checked mathematics.
28. Logic in computer science.
29. Reading list.
30. Watch & read.
31. The constants.
32. The end of the deck.

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