Set Theory

---

About Section

---

Notation

• $A\approx B$ can be read as : There is a bijection between $A$ and $B$.

---

Notes

• Axioms of ZFC
• Von Neumann Ordinals
  • Transitive Sets
• Type of a Set and a Relation
• Cardinals Pre-reqs
• Cardinals
  • Uncountable Cardinalities
  • Cardinal Arithmetic
  • Cofinality
    • Closure of a set under a set of functions
• Hereditarily Finite Sets
• Axiom of Choice and its Variants
• Relative Strength of ZF- and ZF
• Delta0 Formulas
• Absoluteness of Formulas
• Definable Formulas
  • Definable Formulas are Countable
• Ordinal Definable Sets
• Reflection Theorems
  • Proof for Reflection Theorem
• L is a Model of ZFC + GCH
  • Constructable Sets
  • Definable Power Set
  • L Rank of a constructible set
  • L is a model of ZF
  • Axiom of Constructibility
  • L is a Model of ZFC
• Forcing
  • P-Generic classes
  • P-name
  • Valuation of a P-name
  • Generic Extensions of Set Theory Models
  • [[Axioms Satisfied in M[G] ]]
• Continuum Hypothesis

---

MOCs

• Logic
• Independence of CH - Dana Scott
• Homotopy Type Theory

---

References