Timeline for Which model is the minimal pointwise definable model of $\sf ZFC$?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 30, 2022 at 20:41 | comment | added | Joel David Hamkins | But of course, being admissible/recursively inaccessible is mere KP, whereas $\alpha$ gives a ZFC model! So one should think of $\alpha$ as transcending that hiearchy. | |
| Dec 30, 2022 at 20:21 | comment | added | user44143 | That is helpful, and with that I find another helpful answer from you also: mathoverflow.net/a/163835/44143 | |
| Dec 30, 2022 at 20:00 | comment | added | Joel David Hamkins | What would you want to know about it? This $\alpha$ is characterized by being the height of the minimal transitive model of ZFC. It is admissible, recursively inaccessible, etc. etc. | |
| Dec 30, 2022 at 19:58 | comment | added | user44143 | What is known about the minimal $\alpha$? | |
| Dec 30, 2022 at 16:47 | comment | added | Joel David Hamkins | Martin, I would like to thank you for your indefatigable efforts to improve MO with so many helpful edits, resourceful answers on meta, and everything else. Much appreciated! | |
| Dec 30, 2022 at 16:00 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Dec 30, 2022 at 11:56 | comment | added | Asaf Karagila♦ | Yes, of course. I am just clarifying, since some people might not be up to date on technical jargon. :-) | |
| Dec 30, 2022 at 11:52 | comment | added | Joel David Hamkins | Yes, agreed, and in fact, every model of ZFC has a model of ZFC inside it. mathoverflow.net/a/51786/1946 Meanwhile, the phrase "minimal model" is usually taken to refer to the minimal transitive model. | |
| Dec 30, 2022 at 11:48 | comment | added | Asaf Karagila♦ | Arguably there is no minimal model, because if we consider non-transitive models we can get "even smaller" models, in the sense that in $L_\alpha$ there is a model which is not even an $\omega$-model which is pointwise definable. No? | |
| Dec 30, 2022 at 11:16 | vote | accept | Zuhair Al-Johar | ||
| Dec 30, 2022 at 11:12 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Dec 30, 2022 at 11:06 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Dec 30, 2022 at 10:53 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |