Timeline for Can there be an upper bound on definability of cardinal numbers in ZF?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 11, 2018 at 17:18 | vote | accept | Zuhair Al-Johar | ||
| May 11, 2018 at 12:14 | comment | added | Monroe Eskew | Sorry, I'm not explaining well. There are things going on below the surface. The thing in quotes is not a legitimate formula of set theory. What it stands for is, "there is a formula $\phi(v)$ such that its length is $\leq n$, and $\phi(x)$ is true, and there is no other $y$ such that $\phi(y)$ is true." Now, set theory talks about sets and membeship, not about truth directly. Tarski proved that there is no general way to code "is true." However, for each complexity level, there is a code. (not uniform) | |
| May 11, 2018 at 11:39 | history | edited | Monroe Eskew | CC BY-SA 4.0 |
added 25 characters in body
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| May 11, 2018 at 11:39 | comment | added | Monroe Eskew | As $n$ grows, the formula "x is definable by a formula of length $\leq n$" gets longer. There is no uniform definition where we can plug in a number $n$. We have a truth definition for each complexity level, but not for truth as a whole. | |
| May 11, 2018 at 10:45 | history | answered | Monroe Eskew | CC BY-SA 4.0 |