July 25 2014 Progress

Current Reading:

Track 1: HOD as a Core Model by John Steel and Hugh Woodin
Track 2: Large Cardinals from Determinacy by Hugh Woodin
Track 3: Invariant Descriptive Set Theory by Su Gao
Track 4: An Introduction to Core Model Theory by John Steel
Pop Math: Infinitesimal by Amir Alexander

Not too much of interest to report today. HOD is going well, everything is quite familiar and intuitive at the moment. The generation theorem in "Large Cardinals from Detemrinacy is going to be my weekend project. I finished the Glimm-Effros dichotomy chapter in IDST, and I am excited to move onto the general theory of countable Borel equivalence relations. The Introduction to Core Model Theory is, just like the HOD paper, quite familiar and intuitive at this point. It is nice to see the exposition still. Infinitesimal finally got a bit into the math, and now I'm hooked. Amir has elucidated some interesting differences between the Euclidean approach to geometry and the proto-calculus approach. It seems to be the start of rigor vs. inuition. I do, however, find it difficult to follow geometric proofs when they are presented in text. I feel if I am having to struggle with it, the average reader would probably just get lost. Maybe instead of completed geometric diagrams, it would be better to draw the diagram and add the labels in steps. The text brings up an interesting paradox: starting from axioms and chasing deductions is highly stable and very checkable, but the physical intuition seems capable of "justifying" the axioms and simplifying the work, whereas the one thing the axioms can never justify is themselves. Which approach provides deeper knowledge, or better, what's the proper combination of approaches?