Timeline for If a theory speaks of sets that cannot be forced to be parameter free definable, then does this entail a large cardinal property?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2023 at 11:18 | comment | added | Asaf Karagila♦ | It implies there is a class generic extension satisfying AC, so in a sense, yes. | |
| Jan 4, 2023 at 11:16 | comment | added | Zuhair Al-Johar | So, is this principle, a kind of a choice principle? | |
| Jan 4, 2023 at 11:14 | vote | accept | Zuhair Al-Johar | ||
| Jan 4, 2023 at 11:10 | comment | added | Zuhair Al-Johar | Ah! I see. So, T is an effectively generated FOL that extends ZF and that proves that "there is no extension of a model of T to a model of ZFC without adding ordinals". OK! | |
| Jan 4, 2023 at 10:59 | comment | added | Asaf Karagila♦ | Your question is about theories extending ZF. I don't know how you conclude from "$T$ proves that there is no extension of the universe to a universe of ZFC without adding ordinals" to $T$ extends ZFC. | |
| Jan 4, 2023 at 10:39 | comment | added | Zuhair Al-Johar | You mean $T$ is an effectively generated FOL that extends ZFC and that proves that "there is no extension of a model of $T$ to a model of ZFC without adding ordinals". Isn't that inconsistent? Any model of $T$ extends to itself. | |
| Jan 4, 2023 at 10:00 | comment | added | Asaf Karagila♦ | Of $T$????????? | |
| Jan 4, 2023 at 9:33 | comment | added | Zuhair Al-Johar | In the first line "there is no extension of the model" of what theory??? | |
| Jan 4, 2023 at 9:25 | history | answered | Asaf Karagila♦ | CC BY-SA 4.0 |