On CH (After Hamkins)

April 2, 2012

This is my excuse to put this page to use. It all started, more or less, around here:

Moreno, Javier (bluelephant). “Es muy bueno este artículo de Hamkins sobre algo así como sociología de la teoría de conjuntos: http://arxiv.org/abs/1203.4026” 2 April 2012, 3:39 p.m. Tweet.

Villaveces, Andrés (gavbenyos). “@bluelephant lo siento bastante crudo – me parece que Joel simplemente pone en versión impresa cierto consenso, pero falta argumentar” 2 April 2012, 4:32 p.m. Tweet.

(Loosely translated: “This is a very good article by Hamkins on something akin to sociology of set theory” “I find it weak — I think that Joel is simply putting in writing a known consensus, but needs to argue for it more”) Long story short, I feel Andrés is right, but I thought I should elaborate my view, at least somewhat. Originally I considered writing a blog entry, but it quickly became apparent it would grow longer than I can afford time-wise. So, I used twitter instead.

(But there is a serious caveat, namely, it seems that the paper is intended for a general mathematical and philosophical audience, so the omission of technical issues is most likely intentional. Javier even remarked as much.)

What follows is the series of Tweets I posted. It is not a transcription; to ease reading, I have added a couple of links, reformatted the posts rather than continuing with the MLA suggested approach, very lightly edited the most obvious typos, and added a couple of phrases where I felt more clarity was needed. [Edit, April 22: I also removed a line on $MM^{++}$ vs Woodin’s $(*)$, as the proof of the underlying claim has been withdrawn.]

I started at 10:44 p.m., with a warning: “(Technical pseudo-philosophical thoughts for a few posts.)”