The transitive multiverse
There are many discussions on the multiverse of set theory generated by a model. The generic multiverse is given by taking all the generic extensions and grounds of some countable transitive...
View ArticleDangerous knowledge in the Information Age
Back in the days of yore, if one wanted to know mathematics, one would have to go to the university and take a course; or hire a tutor; or go to the library and open a book and learn on their own.And...
View ArticleSome thoughts about teaching introductory courses in set theory
Dianna Crown, the physics woman on YouTube, has posted a video where she is interviewed by her editor about why and how she found herself majoring in physics in MIT.Here is the video:Continue reading...
View ArticleTrust me, I'm a doctor!
Finally!Six months after I had turned in my dissertation, I have finally received the approval on the damn thing.Continue reading...
View ArticleIn praise of failure
I had a recent back and forth on Math.SE with a user that asked whether or not some exercise he found in some textbook is correct. The OP asked not to provide a proof, but rather to confirm if this...
View ArticleNew website!
Welcome to my new website!It is a static website, because I am tired of the WordPress format for a long long time now. So for the occasion, I also got a new domain, karagila.org. Isn't this nice? The...
View ArticleOpen Problems!
I've decided to have a list of open problems on my site. I am no Erdős, nor Hilbert, nor Knuth.But I want my own problems page, and it's my site. So to celebreate the new website, I created just that....
View ArticleCritical Cardinals
Yup. I posted a new paper on arXiv. And if you're one of my three regular readers, you know that I am not going to talk about the paper itself (I leave that to the paper), but rather about the process...
View ArticleDefinable Models Without Choice
Suppose that a parameter formula defines an inner model. Does that inner model satisfy choice?Well, obviously, if choice failed then the answer is no, just by taking \(x=x\). But what if we remove that...
View ArticleFive Star Theorems
Talks. Giving talks. We usually don't give talks about past research. Talks are meant to present recent research, things you've just finished, that you're finishing right now, that you've found out!So...
View ArticleCohen's Oddity
We all know and love Cohen's first model where the axiom of choice fails. It is the O.G. symmetric extension. But Cohen didn't invent the idea on his own, he used Fraenkel's ideas from his work on set...
View ArticlePickles!
Those who know me, also know my strong liking of the amazing Spreewaldhof Get One! pickles (go, get one!). I got one as a present from a friend who visited Germany, and after that, I started obsessing...
View ArticlePreserving Properness
I just posted another problem in the problems page. The prize, by the way, is a bottle of port wine, or equivalent. And I truly hope to make good on that prize.In another problem there, coming from a...
View ArticleIn praise of Replacement
I have often seen people complain about Replacement axioms. For example, this MathOverflow question, or this one, or that one, and also this one. This technical-looking schema of axioms state that if...
View ArticleNew notes online!
I have posted two new lecture notes online. The one is from a course in functional analysis I took in the autumn of 2015/16 with Prof. Matania Ben-Artzi, and the second is from the course I taught in...
View Article7 Easy Hacks to Improve Your Math Skills
Everybody wants to improve their mathematical skills! And quickly, too! Since it's so hard to do just that, I've written down some quick and dirty hacks for quickly improving your mathematical...
View ArticleMethods in Higher Forcing Axioms
Methods in Higher Forcing Axioms (or MEHIFOX, for short) is an experimental workshop hosted in Norwich by David Asperó and myself. You can find the website, right here. This workshop is sponsored by...
View ArticleMethods in Higher Forcing Axioms: The inevitable conclusion
The meeting in Norwich is over. Here are my thoughts.It felt haphazard, without a concrete plan. And that was great. In the first day, Tadatoshi Miyamoto and David (Asperó) presented two problems in...
View ArticleLooking Back at the 2010s
The decade is drawing to a close, and while it is entirely arbitrary, it's a great excuse to look back at this decade.At the end of 2009 I started my senior year as an undergraduate. I both read the...
View ArticleBonus questions
With most people under quarantine, I spent some time going over older files in my computer. Exercise sheets, notes, whatever. Several years ago, when I was a teaching assistant for Itay Kaplan on...
View ArticleCountable sets of reals
One of the classic results of Sierpinski is that if there are as many countable sets of reals as there are reals, then there is a set which is not Lebesgue measurable. (You can find a wonderful...
View ArticleChoose your own adventure (redux)
I've decided to design a small "choose your own adventure". For fatalists. You can also play the interactive version here!.This was originally "in-blog", but I decided that the interactive version is a...
View ArticleYes! Future Leaders Fellowship!
Oh, have I been waiting to tell you something... Yes, I am a Future Leaders Fellow. But as my three regular readers know, this blog is not about announcements, it's about my experience.In early January...
View ArticleOn "trivial" statements
Last night someone asked a question on Math.SE regarding a lemma used in proving certain chain conditions hold when iterating forcing with finite support. The exact details are not important. The point...
View ArticleWhat can you learn about writing papers from cooking pasta?
Those who know me in real life will know that I enjoy cooking. I particularly enjoy cooking pasta. Most authentic Italian recipes are so simple (algio e olio anyone?) that it's just wonderful.I was...
View ArticleSpeak up
I am not here to solve racism. I am not here to solve discrimination. I can't do that. I'm just an early career mathematician, working on very impractical ideas whose influence on society is...
View ArticleWant jobs?
Three years ago I was looking for jobs, I was at the last stretch of my PhD and without clear prospects on what's next. Now I am offering jobs.Unfortunately, this is not as simple as me just looking at...
View ArticleGuest comic: Foundations of Forcing
I recently posted an answer on MathOverflow where I explained a bit about the approaches to forcing in the literature, at least as I experienced them.Hanul Jeon took some of these words, and made them...
View ArticleYouTubers Wanted
As some of you may already know, I was recently awarded a UKRI Future Leaders Fellowship. This is a well-funded project, which is why I can afford hiring postdocs and (once the pandemic is over)...
View ArticleZornian Functional Analysis coming to arXiv!
Back in autumn 2015 I took a functional analysis course with Prof. Matania Ben-Artzi, and he let me write a term paper about uses of the axiom of choice in functional analysis for my final grade. One...
View ArticleFlow and the Partition Principle (6 updates)
Some of you already saw this new preprint on arXiv, and some of you even emailed me about it. I'm reading the paper, but I decided to do something drastic and join Twitter, temporarily, so I can more...
View ArticleFlow and the Partition Principle: Conclusions
So. Just over two weeks ago a paper on arXiv claimed the proof that the Axiom of Choice does not follow from the Partition Principe in \(\ZF\). This is quite a claim, coming out of left field and...
View ArticlePrikry Forcing Online
My new postdoc, Jiachen Yuan, suggested it will be a good idea to have a one-day workshop on Prikry forcing. And I agreed, so we're doing this. You can find more details on the website right here. Here...
View ArticleHindsight: 2020
I know. I already did a looking back post last year when the decade was coming to its inevitable end. But I couldn't pass on a post titled "Hindsight: 2020". And this year was a good year for...
View ArticleFactorial algorithms and recursive thoughts
Recursion: (see recursion). As the joke goes. But that's actually a misnomer, since that would be an ill-founded definition, which is exactly the point where you can't do a recursive definition. I'm...
View ArticleFlow and the Partition Principle II (2 updates)
Well, it seems that there's a new paper about Flow and the Partition Principle on arXiv. This time claiming to prove that in ZF+Atoms the Partition Principle does not imply the Axiom of Choice.I'll...
View ArticleEngaged
No, this isn't some personal blog post.Derek Muller of the Veritasium fame had posted a new video this afternoon. I'm going to spoil the crap out of the video, so you might want to watch it before...
View ArticleChanges
It's been a great ride at the University of East Anglia. I've come there as a postdoc and left with a permanent job. In today's climate, that's nothing to scoff at. But this is the end of this part of...
View ArticleQuestion on Dually Dedekind-infinite sets
I got an email a few days ago from Lucas Polymeris, a Chilean student, who asked me a very nice question. I want to go through the journey I took from that question to the answer.Before we get to the...
View ArticleMultiple Choice
Which answer is the most correct?All of the above.All of the above.All of the above.All of the above.None of the above.Continue reading...
View ArticleEverything Wrong With The Princess Bride
Nothing. Nothing is wrong with that movie. If you haven't watched it in the last couple of weeks, go and watch it tonight.Continue reading...
View ArticleSafe spaces
Sometimes, as a man in mathematics, the topic of diversity comes up. Either discussing with colleagues, or discussing with friends, or whatever. How can we bring more women to mathematics, how can we...
View ArticleHow to prove theorems?
Oddly enough, one of the questions I hear from starting Ph.D. students is "how do you prove theorems?", so let's talk about that.I'm saying "oddly enough", by the way, because first of all, I am...
View ArticleI trained neural nets to do forcing and symmetric extensions
So, I spent the last year training a bunch of neural nets how to do forcing, with and without choice, how to work with symmetric extensions, and how to force over symmetric extensions. It was pretty...
View ArticleWhat is best in science?
It was foretold of a legendary scientist, one who would master all of mathematics, all of physics, all of chemstiry, all of biology, some of engineering, bits of psychology, and none of economics....
View Article120 Years of Choice: First Announcement
We are happy to make the initial announcement for the "120 Years of Choice" conference that will take place in Leeds between the 8th and 12th of July, 2024!We will have a proper website, poster, and...
View Article120 Years of Choice: Registration is open
Continuing from the previous post, we have a website for the conference now, and you can now register for the conference.We are planning to have two poster sessions, and we might be able to offer some...
View Article120 Years of Choice: Final call for registration!
Continuing from last two posts, this is a final reminder to register to 120 Years of Choice. Registration ends next week on the 20th of June.We are very excited about the speakers and the poster...
View ArticleConferences: unsolicited advice
Well, that was quite the week!As the last few posts had possibly clued you in, we hosted a conference in Leeds this past week. We had around 50 participants, including the speakers and poster...
View ArticleThe Lighthouse Problem
This is a piece of advice that I found myself giving to many early career researchers, students, and colleagues supervising and advising those as well. For years, actually.A mathematician, the joke...
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