Timeline for Are superstrong stronger than strongly compact cardinals? (or vice versa)
Current License: CC BY-SA 3.0
15 events
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| Jan 30, 2014 at 19:29 | comment | added | Asaf Karagila♦ | (Also don't worry. The 1000th is meaningless! It's just a finite number. As a set theorist the $\omega$-th, that's the one you should worry about. :-)) | |
| Jan 30, 2014 at 19:25 | comment | added | Joel David Hamkins | I see; I hadn't even noticed the bounty! (I had thought you meant something else by that remark.) But I'm sure that Andrej deserves it. | |
| Jan 30, 2014 at 19:22 | comment | added | Asaf Karagila♦ | Joel, amusingly, the bounty that was meant to lure you to the question was given earlier this morning! | |
| Jan 30, 2014 at 19:19 | comment | added | Joel David Hamkins | @AsafKaragila, I took your advice for my thousandth answer. But now I worry that I should have just answered a technical question, since some MO people don't care for these sweeping topic questions. | |
| Jan 29, 2014 at 21:59 | comment | added | Asaf Karagila♦ | "When MathOverflow gives you lemons..." (a) sell them as Apple Inc. stocks; (b) make lemonade; (c) use them to season your food; (d) give them back, because they are stolen, after all MathOverflow does not own a lemon tree; (e) exactly half of the answers are false, including this one; (f) all of the above. | |
| Jan 29, 2014 at 21:56 | comment | added | Joel David Hamkins | @AsafKaragila, good idea! I was a bit worried I might answer a question and find out afterward that my 1000th answer was some instance of lemonaid. | |
| Jan 29, 2014 at 21:37 | comment | added | Asaf Karagila♦ | Joel, are you saving yourself for a good candidate for the 1k answer? It's like how Shelah skipped the 1000th paper. But where he can skip the index and keep it "reserved", you can't skip the 1000th answer. :-) If so, may I suggest this question as a candidate for the 1k? (I mean, he even set up a bait to lure you in!) | |
| Jan 23, 2014 at 10:01 | comment | added | Asaf Karagila♦ | @Everett: It is ineffable. These things make my jaw drop in awe, and the hair on the back of my neck stand. I am a huge fan of chaos, and my hope is that all the physical laws that we know are wrong beyond belief. Similarly, identity crises are our proof how chaotic and amazing the world of mathematics is. | |
| Jan 23, 2014 at 7:54 | comment | added | Andrés E. Caicedo | $\kappa^+$-strong compactness already takes us beyond what we can currently do by descriptive inner model theoretic methods. | |
| Jan 23, 2014 at 3:48 | comment | added | Everett Piper | @AsafKaragila: I find the "identity crises" phenomenon a little unnerving at times, and certainly an eyesore and unwanted complication when thinking about large cardinals. Would you (or really anyone here on MO) mind explaining why they find "identity crises" among large cardinal concepts "awesome"? My naive thinking on this suggests that one of two things follows from this phenomenon: Either certain large cardinal concepts are too robust to be very meaningful or concrete, or the structure of the universe is not only highly complex, but also a little inelegant. Thoughts? | |
| Jan 23, 2014 at 1:21 | comment | added | Joel David Hamkins | I think that from a strongly compact cardinal one can undertake much of the inner model constructions, but I'm not sure exactly how far you get. But I expect one of the inner model experts on MO to tell us before too long. | |
| Jan 22, 2014 at 19:46 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
Added proof of the theorem
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| Jan 22, 2014 at 19:31 | comment | added | Asaf Karagila♦ | The "identity crises" is awesome. As for the consistency, Mohammad pointed out that indeed we don't know if superstrong are as strong as strongly compact (in which case it will solve the problem in the Battle of the Compacts); but do we know anything on the other direction in terms of consistency? | |
| Jan 22, 2014 at 19:30 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 417 characters in body
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| Jan 22, 2014 at 19:17 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |