Notes
Here I store some notes. I prepared these notes to help myself understand certain topics, for presentation at seminars, or recording half-baked research ideas. They have not been checked thoroughly and certainly contain typos and errors to taste.
Descriptive Set Theory
- Perfect set theorems for closed and analytic sets
- Normal forms for \(\Sigma^1_1\), Luzin’s arithmetic example, and prewellorderings
- There is no Borel 2-coloring for the irrational rotation graph
- Mouse capturing phenomena at \(\Delta^1_1\) and \(\Delta^1_2\)
- The largest \(\Pi^1_1\) thin set as a sharp
Set Theory
- 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)