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Mathematics
Mathematical Logic
1. Introduction to Mathematical Logic
2. Propositional Logic
3. First-Order Logic
4. Model Theory
5. Computability Theory
6. Incompleteness Theorems
7. Axiomatic Set Theory
8. Proof Theory
9. Modal Logic
10. Intuitionistic Logic
11. Higher-Order Logic
10.
Intuitionistic Logic
10.1.
Philosophical Foundations
10.1.1.
Constructive Mathematics
10.1.2.
Rejection of Law of Excluded Middle
10.1.3.
Brouwer's Intuitionism
10.2.
Syntax of Intuitionistic Logic
10.2.1.
Logical Connectives
10.2.2.
Quantifiers
10.2.3.
Formation Rules
10.3.
Semantics of Intuitionistic Logic
10.3.1.
Brouwer-Heyting-Kolmogorov Interpretation
10.3.2.
Kripke Semantics for Intuitionistic Logic
10.3.3.
Topological Semantics
10.4.
Proof Theory of Intuitionistic Logic
10.4.1.
Natural Deduction for Intuitionistic Logic
10.4.2.
Sequent Calculus for Intuitionistic Logic
10.4.3.
Cut-Elimination
10.5.
Relationship to Classical Logic
10.5.1.
Double Negation Translation
10.5.2.
Gödel-Gentzen Translation
10.5.3.
Embedding Results
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9. Modal Logic
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11. Higher-Order Logic