Notes
These range from expository to teaching to research notes. They have not been checked thoroughly and certainly contain typos and errors to taste. Consume at your own risk ;)
Descriptive Set Theory
- Absolutely \(\Delta^1_2\) sets have constructible generalized Borel codes
- Descriptive complexity measure-preserving transformations with roots
- Perfect set theorems for closed and analytic sets
- Normal forms for \(\Sigma^1_1\), Luzin’s arithmetic example, and prewellorderings
- Mouse capturing phenomena at \(\Delta^1_1\) and \(\Delta^1_2\)
- The largest \(\Pi^1_1\) thin set as a sharp
Definable Equivalence Relations
- Finite-index extensions of essentially free countable Borel equivalence relations (Answers problem 11.4 in Kechris’s CBER book)
- A locally countable coanalytic graph not generated by countably many Real-Ordinal definable functions
- Two questions on \(E_0\)-like generic equivalence (2026 Tianyuan Mathematical Logic Problem List 8.1 and 8.3)
- There is no Borel 2-coloring for the irrational rotation graph
Set Theory
- Second-Order Constructibility and HOD Without AC
- Introduction to Inaccessible Cardinals
- Measurable Cardinals and Elementary Embeddings
- Product Forcing, Iterated Forcing, Continuum Coding, and Forcing the Ground Axiom
Teaching Materials
- Prerequisites on Large Cardinals (For Fudan Logic Summer School 2022: Large Cardinals beyond Choice)
- Decision tree method for filling out truth tables (teaching material for intro logic)