In strange news (and alsos)
Aug. 2nd, 2008 07:31 pmVlad attempted to get Keith Conrad to autograph his pants. He apparently got Keith to reluctantly initial them.
(Explanation perhaps later.)
Also the other day I played the most disappointing 2 rounds of Sticheln ever. Everybody got a positive score.
(I also finally played Bang! the other day. OK, I guess, but really random and there's not a lot you can really do coherently. As far as silly take-that games go, I'd rather play Kung Fu Fighting.)
So I was telling Josh about the infinitary combinatorics thing Babai did last summer, and as a result measurable cardinals came up, and of course I mention "except ℵ0" and somehow we get to the topic of large cardinals in general, and how ℵ0 really is a large cardinal, we just declare it to exist with the axiom of infinity; so it's a large cardinal except by fiat. (Well, I don't know just what large cardinal axioms it satisfies, but it's certainly measurable and that's pretty high up there on Wikipedia's list.) And apparently Josh never realized this before - he just thought that ℵ0 behaves a lot like large cardinals, he didn't realize it is one except that it's one we can all agree exists, and so the axiom of infinity really is the first large cardinal axiom. And I mention what I saw on Wikipedia, that apparently people justify adding large cardinal axioms by analogy to the axiom of infinity, and Josh says yeah, he'd seen that before, but he didn't really understand it. He then proceeded to go around telling everyone, "Hey! Did you realize that ℵ0 is a large cardinal that we declare to exist?"
(Also, I brought up 2κ↛(κ+,κ+), and I said I had proved it, but I was trying to reconstruct my proof and I don't think it was right. But now I've proved it, I'm pretty sure.)
-Harry
(Explanation perhaps later.)
Also the other day I played the most disappointing 2 rounds of Sticheln ever. Everybody got a positive score.
(I also finally played Bang! the other day. OK, I guess, but really random and there's not a lot you can really do coherently. As far as silly take-that games go, I'd rather play Kung Fu Fighting.)
So I was telling Josh about the infinitary combinatorics thing Babai did last summer, and as a result measurable cardinals came up, and of course I mention "except ℵ0" and somehow we get to the topic of large cardinals in general, and how ℵ0 really is a large cardinal, we just declare it to exist with the axiom of infinity; so it's a large cardinal except by fiat. (Well, I don't know just what large cardinal axioms it satisfies, but it's certainly measurable and that's pretty high up there on Wikipedia's list.) And apparently Josh never realized this before - he just thought that ℵ0 behaves a lot like large cardinals, he didn't realize it is one except that it's one we can all agree exists, and so the axiom of infinity really is the first large cardinal axiom. And I mention what I saw on Wikipedia, that apparently people justify adding large cardinal axioms by analogy to the axiom of infinity, and Josh says yeah, he'd seen that before, but he didn't really understand it. He then proceeded to go around telling everyone, "Hey! Did you realize that ℵ0 is a large cardinal that we declare to exist?"
(Also, I brought up 2κ↛(κ+,κ+), and I said I had proved it, but I was trying to reconstruct my proof and I don't think it was right. But now I've proved it, I'm pretty sure.)
-Harry
