User:HarrisonTotty/Books/Mathematics - Foundations and Philosophy

Foundations & Philosophy

 * Overview
 * Mathematics
 * Foundations of mathematics
 * Philosophy of mathematics
 * Metamathematics
 * Language of mathematics
 * Logic
 * Mathematical logic
 * Set theory
 * Model theory
 * Proof theory
 * Computability theory


 * Set Theory
 * Zermelo–Fraenkel set theory
 * Set (mathematics)
 * Union (set theory)
 * Intersection (set theory)
 * Complement (set theory)
 * Symmetric difference
 * Cartesian product
 * Power set
 * Algebra of sets


 * Model Theory
 * Structure (mathematical logic)
 * Type (model theory)


 * Proof Theory
 * Mathematical proof
 * Mathematical induction
 * Formal language
 * Axiom
 * Theorem
 * Logical consequence
 * Direct proof
 * Contraposition
 * Proof by contradiction
 * Constructive proof
 * Proof by exhaustion
 * Probabilistic method
 * Combinatorial proof
 * Gödel's incompleteness theorems