# Notes

Here I store some notes. I prepared these notes to help myself understand certain topics or for presentation at seminars. They have not been checked thoroughly and certainly contain typos of various amount.

### Set Theory

- Introduction to Inaccessible Cardinals
- Measurable Cardinals and Elementary Embeddings
- Product Forcing, Iterated Forcing, Continuum Coding, and Forcing the Ground Axiom
- (in Chinese) Magidor Characterization of Supercompactness, and Generic Ultrapowers

### 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

### Undergrad Teaching Material

- (in Chinese, for general public) Infinity, Paradox, and Limits of Thoughts
- (teaching material for intro logic) Decision tree method for filling out truth tables