Mathematics

• Introduction to Forcing
• Categorical Trace
• The Measure Problem and the Continuum Hypothesis
• Categorical Proofs of the Commutative Law, Distributive Law, and Exponential Law
• Suslin's Problem and the Diamond Principle
• Euler-Poincaré Theorem
• Club Sets and Stationary Sets
• Are Mathematics and Ethics in the Same Boat?: The Evolutionary Challenge
• Simplicial Homology
• The Continuum Hypothesis for Closed Sets and Borel Sets
• Cardinal Arithmetic
• Proof of Tychonoff's Theorem Using Ultrafilters
• Ideals and Filters in Boolean Algebraic Structures
• Stone-Čech Compactification
• The Urysohn Lemma and Urysohn Metrisation Theorem
• Stone Spaces and the Compactness Theorem
• Quantifier Elimination
• Saturated Structures and the Completeness of Real Closed Fields
• η Sets
• Robinson, Craig, and Beth's Theorems
• Regular Cardinals, Singular Cardinals, and Inaccessible Cardinals
• Homomorphisms, Embeddings, and Elementary Embeddings
• A Colouring Problem Equivalent to the Continuum Hypothesis
• Notes on the Definition of Cardinality
• Infinite Prisoner Hat Problem
• The Łoś-Tarski Preservation Theorem
• Completeness Theorem and Löwenheim-Skolem Theorem
• Notes on the Seifert-van Kampen Theorem
• The Difference Between Product and Box Topologies, and Direct Product and Direct Sum from a Categorical Perspective
• Modal Logic
• Yoneda Lemma
• Notes on Tensor Products
• Lebesgue Measurable Sets and Borel Measurable Sets
• Construction of Measures via Carathéodory's Theorem
• Definitions of Algebra and Measure
• Ramsey Numbers and the Infinite Ramsey Theorem
• Adjoints, Normal Transformations, and the Spectral Theorem
• Three Approaches to Adjoints
• Can the Mind Be Reduced to a Machine: Gödel's Disjunction and the Penrose-Lucas Argument
• Arithmetic Hierarchy
• Notes on Multiplicative Groups and Order: Fermat's Theorem on Primes and Wilson's Theorem
• Defining Gödel Numbers in Peano Arithmetic via the Beta Function
• Łoś's Theorem
• Fréchet Filters and Nonstandard Natural Numbers
• Proving the Uncountability of Real Numbers Without the Diagonal Argument
• The Cantor-Bendixson Theorem and Polish Space
• An Intuitive Understanding of Adjoints
• Consistency of the V = L Axiom
• Transfinite Induction and Transfinite Recursion
• Compactness and Nets
• The Baire Category Theorem
• Trichotomy and Completeness of Ordinals
• Set-theoretic Definitions of Rational and Real Numbers
• Cantor–Schröder–Bernstein Theorem
• List of ZFC Axioms