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