Timeline for Intuitionistic set-theoretic geology
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 26 at 0:56 | comment | added | Hanul Jeon | I am unsure if the notion of ground makes sense in a constructive setting. A set-theoretic universe without LEM is quite wild: For example, ordinals need not be linearly ordered, and the powerset of 2 can be uncountable (in the sense that there is no onto function from $\omega$.) I also have not seen any materials considering a generic extension of a universe without LEM, even on materials considering intuitionistic forcing. | |
| Aug 26 at 0:56 | comment | added | James E Hanson | @HanulJeon Ah that's news to me. Thank you for letting me know. | |
| Aug 26 at 0:53 | comment | added | Hanul Jeon | @JamesEHanson Richard Matthews proved in his thesis (Theorem 5.5.1) that $\mathsf{IZF}$ is consistent with $\mathrm{Ord}\neq \mathrm{Ord}\cap L$, so $\mathsf{IZF}+\lnot\mathsf{LEM}+V\neq L$ is consistent. | |
| Aug 24 at 17:10 | comment | added | James E Hanson | This is a nice question but given the state of knowledge about inner models in constructive set theory (i.e., there is at least no published resolution of whether $\neg \mathsf{LEM}$ implies $V=L$ over $\mathsf{IZF}$) and the state of research regarding large cardinals (i.e., Mahlos have been looked at and I believe some people are looking at measurables), I feel pretty confident in saying that we're nowhere near having the kind of clear picture that would be needed to address this question. | |
| Aug 24 at 9:17 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Aug 24 at 6:43 | history | asked | Ember Edison | CC BY-SA 4.0 |