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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
11.
Higher-Order Logic
11.1.
Syntax of Higher-Order Logic
11.1.1.
Type Theory
11.1.2.
Lambda Abstraction
11.1.3.
Comprehension Principles
11.2.
Semantics of Higher-Order Logic
11.2.1.
Standard Semantics
11.2.2.
Henkin Semantics
11.2.3.
General Models
11.3.
Metatheory of Higher-Order Logic
11.3.1.
Completeness and Incompleteness
11.3.2.
Undecidability
11.3.3.
Expressive Power
11.4.
Applications
11.4.1.
Foundations of Mathematics
11.4.2.
Computer Science Applications
11.4.3.
Automated Theorem Proving
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10. Intuitionistic Logic
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1. Introduction to Mathematical Logic