Timeline for If we have a class like $L$ but allowing a set number of unbounded quantifiers, is it strict superset of $L$?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2020 at 22:29 | history | edited | Christopher King | CC BY-SA 4.0 |
deleted 1 character in body
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| Nov 6, 2020 at 12:52 | vote | accept | Christopher King | ||
| Nov 5, 2020 at 18:43 | answer | added | Joel David Hamkins | timeline score: 7 | |
| Nov 5, 2020 at 17:06 | comment | added | Christopher King | @NoahSchweber ah yes, you are correct. My definition didn't make sense. I fixed it so that the model includes $x_1, x_2,$ and $x_3$. | |
| Nov 5, 2020 at 17:04 | history | edited | Christopher King | CC BY-SA 4.0 |
Fix definition
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| Nov 5, 2020 at 14:32 | review | Close votes | |||
| Nov 10, 2020 at 3:08 | |||||
| Nov 5, 2020 at 4:08 | comment | added | Noah Schweber | Well you can't write e.g. "$X\models\varphi(x)$" if $x\not\in X$. Also, I don't actually see why this needs to produce a model of $\mathsf{ZF}$. | |
| Nov 5, 2020 at 4:05 | comment | added | Christopher King | @NoahSchweber in the definition of $L$, you essentially have bounded quantifiers, bound to $X$. The $x_1, x_2, x_3$ do not need to be in $X$. Perhaps the way I phrased it was confusing. | |
| Nov 5, 2020 at 3:56 | comment | added | Noah Schweber | I don't understand: in what sense does the definition of $L$ only permit bounded quantifiers? The definable powerset uses all formulas. (Or in your definition of $\mathsf{Def}^{\Sigma_3}(X)$ are $x_1,x_2,x_3$ not required to be from $X$?) | |
| Nov 5, 2020 at 3:32 | history | asked | Christopher King | CC BY-SA 4.0 |