ginnungagap

I know Talagrand because some of his work comes up in topological dynamics (work around Rosenthal's l¹-dichotomy culminating in the Bourgain-Fremlin-Talagrand dicothomy for compact sets of Baire class 1 functions), but I had no idea he has such accomplishments in other fields! Impressive

Wow that was fast, how does that safety system work?

> This is simply false, as I already explained.

I'm sorry but this is just wrong. Since you seem to like Shapiro's book more than traditional set theory books let me quote from page 144 that the existence of an uncountable set is a theorem of ZFC: "Let C be the statement of Cantor's theorem. It entails that the powerset of the collection of finite ordinals is not countable. Since C is a theorem of first-order ZFC..."

Also this is not how the metatheory is understood in mathematics, not even in Shapiro's book, who dedicates two whole chapters to the metatheory

It is a theorem of ZFC that uncountable sets exist and every model of ZFC will have a set that the model believes to be uncountable. It doesn't matter than the metatheory might believe that model to be countable (why should the metatheory have the correct notion of what it means to be countable anyway?).

Of course, but what is your point?

Löwenheim-Skolem gives you a countable elementarily equivalent submodel (assuming you're working in a theory in a countable language, otherwise it gives you an elementary substructure of the same cardinality of the language at best), but plenty of interesting properties of familiar mathematical objects cannot be captured by a first-order theory and are not preserved by elementary equivalence, completeness of the reals being the standard example

Beginners do that exactly until the first time they have a render crash halfway through, then they learn about rendering each frame as an image (yes I learned this lesson the hard way)

If to understand D you need to know both B and C, each of which requires familiarity with A, the graph is not a tree

Those seem to be working! Thanks!

Italian here, I was trying to access anna's archive today (and libgen as well) without success, is there any easy workaround?

Oh I see, I was confused because I didn't mention PPE in my comment, maybe you meant to answer to the other top level comment which does use this abbreviation!

I'm not sure what's your point, that hardly looks like a math heavy degree

Weird to write an article about Liz Truss as a math snob (a description that seems rather stretched to be honest) without mentioning that her father, John Truss, is a fairly well known model theorist! (Even though they're not really very close from what I've been told by students of the latter)

The pdf includes famous altered images from the 2006 Lebanon war but not other well known staged ones from the same conflict, so maybe the author does consider staging a different category?