July 15 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: A Theorem of Woodin on Mouse Sets by John Steel
Bonus Track: Model Theory by Chang and Kiesler
Pop Math: Infinitesimal by Amir Alexander

I finally bothered to look up the correct name for track 1, I should have done it earlier but I was lazy. It's more correct as technically the paper talks about L(R) and L[x,G]. Anyways, I covered pseudo-normal-iterates today in detail. My gut feeling is that this definition, like many others in this subfield is a highly refined, exactly what works definition. But the idea of describing the models that show up when following a strategy L[x,G] can't see in a way that L[x,G] can see is very much the same as the approach to HOD in L(R) and I find it intuitive.

Track 2 was not very exciting today, but I am building up important groundwork. It's just a generalization of the Turing cone measure. I say "just," but the generalization is intuitive and the results are strong. I now remember that I did start to cover strategic determinacy. I don't have a good feeling for this definition yet, I think it will require a good amount of meditation and use before it becomes clear, the excellent exposition in the paper not withstanding.

For track 3, I learned about the Effros dichotomy. I know this is an important result, and I am excited to see the applications of it to come. For whatever reason this material feels intuitive. Its probably because I have a good amount of DST experience.

Again I couldn't bring myself to look at track 4 today. I'm seriously considering leaving it for now and coming back to it when I can better understand its relevance. Its annoying to leave the paper so nearly finished, but I may have to follow my gut. If I do leave it I will start reading on the core model induction.

On the bonus track I waded halfway through the section on nonstandard universes. Chang has a comment about not liking the term nonstandard analysis, which he wants to replace with Robinsonian analysis. I get the historical context he's coming from, but the reality is that the method of analysis is nonstandard, and I don't see the name changing any time soon. So far the material has been review, but a second look never hurts.

"Infinitesimal" moved on to start telling the story of how math became more of a focus for the Jesuits. The story of the inception of the Gregorian calendar is fascinating, but I find this historical background to maybe be a bit too long. I hope the book starts getting to the controversy soon.