Set Theory

• Introduction to Forcing
• The Measure Problem and the Continuum Hypothesis
• Suslin's Problem and the Diamond Principle
• Club Sets and Stationary Sets
• The Continuum Hypothesis for Closed Sets and Borel Sets
• Cardinal Arithmetic
• Saturated Structures and the Completeness of Real Closed Fields
• η Sets
• Regular Cardinals, Singular Cardinals, and Inaccessible Cardinals
• A Colouring Problem Equivalent to the Continuum Hypothesis
• Notes on the Definition of Cardinality
• Consistency of the V = L Axiom
• Transfinite Induction and Transfinite Recursion
• Trichotomy and Completeness of Ordinals
• Set-theoretic Definitions of Rational and Real Numbers
• Cantor–Schröder–Bernstein Theorem
• List of ZFC Axioms