nLab set theory - contents

set theory

• fundamentals of set theory
  • propositional logic
  • first-order logic
  • typed predicate logic
  • membership relation
  • propositional equality
  • set, element, function, relation
  • universe, small set, large set
• material set theory
  • membership relation, propositional equality, axiom of extensionality
  • pairing structure, axiom of pairing
  • union structure, axiom of union
  • powerset structure, axiom of power sets
  • natural numbers structure, axiom of infinity
• presentations of set theory
  • first-order set theory
  • unsorted set theory
  • simply sorted set theory
    • one-sorted set theory
    • two-sorted set theory
    • three-sorted set theory
  • dependently sorted set theory
  • structurally presented set theory
• structuralism in set theory
  • material set theory
    • ZFC
    • ZFA
    • Mostowski set theory
    • New Foundations
  • structural set theory
    • categorical set theory
      • ETCS
        • fully formal ETCS
        • ETCS with elements
        • Trimble on ETCS I
        • Trimble on ETCS II
        • Trimble on ETCS III
      • structural ZFC
    • allegorical set theory
      • SEAR
• class-set theory
  • class, proper class
  • universal class, universe
  • category of classes
  • category with class structure
• constructive set theory
• algebraic set theory