July 14 2014 Progress

Current Reading:

Track 1: HOD in L(R) 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: A Theorem of Woodin on Mouse Sets by John Steel
Bonus Track: Model Theory by Chang and Kiesler
Pop Math: Infinitesimal by Amir Alexander

Today was good work day, not perfect, but good. "HOD in L(R)" continues to be interesting, but I find it difficult to keep the myriad versions of iterability straight in my head. I'm trying to form some intuition for the various forms, but I suspect that will come later. As for "Large Cardinals from Determinacy," I find the level of generality breathtaking, and I haven't even reached the most general point yet. What's nice is how this and "HOD in L(R)" are overlapping right now. My studies for a while now have been centered on L(R), its nice to be able to spend time in HOD. "Invariant Descriptive Set Theory" has finally started to get into gear, today I covered E_0 and there are interesting Dichotomies to come. Track 4 got no love today unfortunately.

I finally reached the section in "Model Theory" where they cover regular filters. As much as I love my complete filters, studying interesting filters that more naturally exist has its own appeal. Tomorrow I cover the section on nonstandard universes, I hope the more complete model theory background will help make these wonderful objects more accessible. Finally I got through the first chapter of "Infinitesimal." The book certainly starts off tediously enough, I felt as though I were watching a discovery channel documentary for a while there. Finally though he starts telling the story instead of trying to convince me the story is worth telling, and the first chapter is a fascinating, if brief, history of the fracturing of the Catholic church and consequent formation of the Jesuit order. No math has been discussed yet, but I do feel like I understand the sociological motivations of the anti-infinitesimal side a bit better. As far as learning what kind of writing allows a math book to be popular, I fear I am so far only able to reach the sad conclusion that excluding the math and emphasizing the people and the history is the answer.