Asaf Karagila
I don't have much choice...

Blog posts from 2018

Definable 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 option. Namely, if the inner model is not the entire universe, then choice holds. Continue reading...

Critical 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 leading to it. If you don't care, that's fine, the paper is on arXiv and you can check the Papers section of the site to see if it's been published or whatnot.

So, this one has been on the back burner for a while. And it actually started as two separate projects that merged and separated and merged again. Continue reading...

Open 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. For the first couple of problems, I've chosen to focus on the axiom of choice. And I don't think that I have much choice, but to keep that interest running. But I can promise that this is not the only type of problems that I will add there. Continue reading...

New 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 only domain and all the links should work, at least for the foreseeable future. So there's nothing to worry about linkrot for now. But please do update your links! Continue reading...

In 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 statement is at all provable. When I asked why not just try and prove the damn thing, the reply was that if there is a typo or a mistake and the statement is in fact not provable, then they would have wasted their time trying an impossible task.

Well. Actually no. When I was a dewy eyed freshman, I had taken all my classes with 300 students from computer science and software engineering (Ben-Gurion University has changed that since then). Our discrete mathematics professor was someone who was renowned as somewhat careless when it comes to details in questions and stuff like this (my older brother took calculus with the same professor about ten years before, one day he didn't show up to class, when my brother and two others went to see if he is at his office, he was surprised to find out that today is Tuesday). Continue reading...