Timeline for Seeing what gets Harvey Friedman's "tangible incompleteness" principles into large cardinal territory
Current License: CC BY-SA 4.0
20 events
| when toggle format | what | by | license | comment | |
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| Oct 13, 2023 at 20:26 | comment | added | James E Hanson | @MaliceVidrine I'm currently working through Finite Functions and the Necessary Use of Large Cardinals, which Friedman published around the same time. Broadly speaking the argument there involves using a strong finitary Ramsey's theorem and compactness to build a structure that has the ability to code some basic set theory and has a special cofinal indiscernible sequence of elements. This indiscernible sequence then gives you enough reflection to show that the interpreted model of basic set theory satisfies ZFC. I would guess that the story in this paper is broadly similar. | |
| S Jan 29, 2021 at 8:01 | history | bounty ended | CommunityBot | ||
| S Jan 29, 2021 at 8:01 | history | notice removed | CommunityBot | ||
| S Jan 21, 2021 at 6:01 | history | bounty started | Noah Schweber | ||
| S Jan 21, 2021 at 6:01 | history | notice added | Noah Schweber | Draw attention | |
| S May 6, 2020 at 0:01 | history | bounty ended | CommunityBot | ||
| S May 6, 2020 at 0:01 | history | notice removed | CommunityBot | ||
| S Apr 27, 2020 at 22:04 | history | bounty started | Malice Vidrine | ||
| S Apr 27, 2020 at 22:04 | history | notice added | Malice Vidrine | Draw attention | |
| Jan 23, 2020 at 9:08 | comment | added | Malice Vidrine | @TimothyChow - I suppose I didn't totally answer your question: I'm most interested in the line of thought behind formulating statements of this kind, less with k-SRP cardinals specifically. There's clearly something that leads Friedman to choose stable maximal emulators (or various other similar objects) as good objects for bumping up consistency strength, but I have no clue what the guiding idea is. | |
| Jan 21, 2020 at 18:18 | comment | added | Malice Vidrine | @TimothyChow - I'm still working my way back through his previous papers, so that's a work in progress. Right now the earliest I'm passably familiar with is Subtle Cardinals and Linear Orderings, and I'm working on a couple of papers from '96, but I've by no means exhausted his bibliography in between. Perhaps I will email him, though. | |
| Jan 21, 2020 at 17:23 | comment | added | Timothy Chow | Your best bet might be to contact Friedman directly by email. One question I have is whether you've worked through any of Friedman's earlier work in this area? Are you just trying to get a feeling for Friedman's general methodology for proving statements of this kind? Or do you have a good grasp of his earlier work and are just having trouble with $k$-SRP cardinals specifically? | |
| Jan 16, 2020 at 15:55 | history | edited | Malice Vidrine | CC BY-SA 4.0 |
added 73 characters in body
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| Jan 16, 2020 at 8:30 | comment | added | Malice Vidrine | @JoelDavidHamkins - I suspected I was misstating that; this is still deeply new territory for me. But that does help me start to see where I'm going wrong... | |
| Jan 16, 2020 at 8:20 | comment | added | Joel David Hamkins | "...their guaranteed existence implies the existence of large cardinals" is not right, because no arithmetic statement can imply the existence of large cardinals. You mean to imply the consistency of the existence of the large cardinals. | |
| Jan 16, 2020 at 7:24 | history | migrated | from math.stackexchange.com (revisions) | ||
| Jan 15, 2020 at 4:09 | comment | added | Noah Schweber | Not sure, honestly - crossposting immediately is generally frowned on, but in this case I would imagine deleting here and asking there should be fine (since it hasn't been up here for long enough for a move to be construed as wasting someone's time). But that's just my opinion; certainly there's no harm asking it here and moving to MO after a bit if no answers show up. | |
| Jan 15, 2020 at 4:08 | comment | added | Malice Vidrine | @NoahSchweber - Noted. What's good etiquette on moving it over? | |
| Jan 15, 2020 at 4:07 | comment | added | Noah Schweber | This might be more appropriate at mathoverflow - this is some seriously technical material (and I think people capable of answering it might be more likely to see it there). | |
| Jan 15, 2020 at 3:52 | history | asked | Malice Vidrine | CC BY-SA 4.0 |