August 28 Progress

Reading Courses:

• Structural Consequences of AD by Stephen Jackson
• HOD as a Core Model by John Steel and Hugh Woodin

Other Reading:

• Invariant Descriptive Set Theory by Su Gao
• The Core Model Iterability Program by John Steel
• Non-Standard Analysis for the Working Mathematician
• Counting Equivalence Classes for Co-\kappa-Souslin Equivalence Relations by Leo Harrington and Sarahon Shelah
• Infinitesimal by Amir Alexander

The past week and a half has been a bit crazy, this is the first of class and there was a lot of preparing to do.But the structure of having to be on campus for meals and teaching seems to be helping my productivity. Dr.Gao's chapter on analytic equivalence relations has me excited about possible interactions between determinacy theory and the theory of equivalence classes. I talked to Dr.Jackson about it and he pointed me to the paper by Harrington and Shelah. If I can tame it, I will present it to the graduate logic group. The first chapter of "Non-Standard Analysis for the Working Mathematician" has me annoyed, I think their half-job of describing first order logic is more complicated to think about than the real thing, and it seems they only do it to be able to Prove Los's theorem, which they do in full generality later anyways. I had a good meeting with Dr.Jackson on Tuesday, and I am reminded to always always always try to draw a picture first. The core model iterablity is as hard as advertised, but I am pushing through. Finally, Infinitesimal has taught me that Thomas Hobbes thought he had squared the circle, despite all of his proofs being debunked. That should be filed under great historical blunders.