What is Foundations of Mathematics?
Naive Set Theory
- Cantor's Diagonal Method
Paradoxes
- Russell's Paradox
- Burali-Forti Paradox
- Cantor's Paradox
Formal Systems
- Formal Language
- Axioms and Inference Rules
- Axiomatic Method
- Proof Theory
Axiomatizations
- Set Theory
--
Zermelo-Fraenkel Axioms
--
Neumann-Bernays-Gödel Set Theory
--
Continuum Hypothesis
- Geometry
--
Euclid's Postulates
--
Hilbert's Axioms
--
Non-Euclidean Geometries
- Arithmetic
- Other Formal Systems
Mathematical Logic
- Propositional Calculus
- First-Order Predicate Calculus
--
Normal Forms
--
Herbrand Theorem
- Intuitionistic Logic
- Higher-Order Logic
- Modal Logic
- Equational Logic
- Logic Systems
--
Natural Deduction
--
Sequent Calculus
Completeness and Consistency
- Gödel's Incompleteness Theorem
Intuitionism
- Constructive Mathematics
Model Theory
- Löwenheim-Skolem Theorem
- Skolem Paradox
Computability
- Computation Models
- Unsolvability
- Lambda Calculus