Timeline for Good set theory in which to study ordinal-indexed sequences?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 23, 2015 at 8:08 | vote | accept | goblin GONE | ||
| Oct 6, 2012 at 21:53 | comment | added | Asaf Karagila♦ | Yes, classes are not real elements in ZFC but it doesn't mean we cannot say things about them, and prove things about them. There are a lot of delicate points, but it is mathematically valid to do that. This is like saying that you cannot prove anything in PA about infinite sets (e.g. all even numbers can be divided by two). I wrote some math.SE answers about this topic, math.stackexchange.com/a/137335/622 math.stackexchange.com/a/139337/622 math.stackexchange.com/a/173002/622 | |
| Oct 6, 2012 at 21:09 | comment | added | goblin GONE | "I suggest that you work on your set theory a bit first and learn how classes are dealt with within ZFC." Yes, I would like to do that, but I thought classes were NOT dealt with within ZFC? I would like to study a set theory that actually allows these sorts of sequences. | |
| Oct 6, 2012 at 10:00 | comment | added | Asaf Karagila♦ | Yianni, note that $R$ is $V$, the universe, in ZF due to the axiom of regularity which implies $x\notin x$ for all $x$. It is not clear what you are planning to do while studying; it may be sufficient to use ZF after all. I suggest that you work on your set theory a bit first and learn how classes are dealt with within ZFC. | |
| Oct 6, 2012 at 1:30 | comment | added | goblin GONE | I was actually hoping to avoid classes, because I was hoping to model "large" sets (or "classes") as ordinal-indexed sequences as follows. Suppose one wishes to study $R = \{x | x \notin x\}$, for example. One would instead study $R_{\alpha} = \{x \in V_{\alpha} | x \notin x\}$. (I'm not sure of this idea works, though.) A "large set" or "proper class" would be an object such that this sequence never becomes constant. That being said, perhaps a class theory such as NBG would be a good context in which to study this idea. | |
| Oct 6, 2012 at 0:56 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |