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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
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