Timeline for Does every model of ZF-foundation have an extension, with no new well-founded sets, where every set is bijective with a well-founded set?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 28, 2019 at 6:01 | comment | added | Asaf Karagila♦ | @Paul: Models with atoms can be seen as models of ZF-Foundation, and the atoms are generators for the ill-founded part (using, quite fittingly Quine atoms for the atoms). In your work with Saharon you make a model where the pure sets, or the well-founded part, satisfies ZFC, and you cannot extend the model with atoms to a model of ZFC-Foundation without collapsing cardinals, which is the same as adding well-founded sets (sets of ordinals). | |
| May 24, 2019 at 17:02 | comment | added | Paul Larson | I have seen this, but I haven't figured out the relationship between the question and our paper. There is some overlap between the remarks in Section 4 of our paper and some relatively recent work of @Joel (but I just looked and didn't find the related work on Joel's site). | |
| May 24, 2019 at 14:54 | history | edited | Asaf Karagila♦ | CC BY-SA 4.0 |
Clarified credits
|
| May 17, 2018 at 7:20 | comment | added | Asaf Karagila♦ | @David: Correct. | |
| May 17, 2018 at 7:20 | comment | added | David Roberts♦ | @Asaf do you mean this: users.miamioh.edu/larsonpb/ZFAC.pdf ? | |
| May 15, 2018 at 14:07 | comment | added | Asaf Karagila♦ | There is a preprint available on Paul's website. I don't like the approach Shelah takes to models with atoms, so I found it very confusing to try and understand what he actually did there. I understand the idea, but if I ever decide that I want to find out the exact details, I would probably just sit and try to come up with the proof myself. There's a good chance Paul will see this question, and then he might be able to shed some light on the topic. | |
| May 15, 2018 at 14:03 | comment | added | Joel David Hamkins | Great! Could you explain the construction a little more fully? And do you have a reference? My intended extension concept was end-extension with no new well-founded sets. So in particular, collapsing (well-founded) cardinals would not be allowed. | |
| May 15, 2018 at 13:56 | history | answered | Asaf Karagila♦ | CC BY-SA 4.0 |