Set Theory

This section covers ZFC set theory, and constructs the foundations of mathematics from 9 axioms. Topics include basic properties of sets, functions and relations and ordinal and cardinal numbers.

Table of Contents

• Logic
  • History
  • Logic / Language
• Basic Axioms and Operations
  • Primitive notions / Set containment
  • Preview of Axioms X
  • Axioms of Extension and Specification
  • Subsets
  • Intersections and Differences X
  • Axiom of Pairing X
  • Axiom of Union X
  • Axiom of Powerset X
  • Cartesian Sets X
  • Axiom of Regularity X
• Relations and Functions
• Ordinal Numbers
• Cardinal Numbers
  • Equinumerosity X
  • Equinumerosity Arithmetic X
  • Equinumerosity Ordering
    
  • Finite Sets

References

Naive Set Theory - Paul Hermas - 1960