Talk:Axiom of dependent choice

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Surely, there are a gazillion axioms of set theory that assert the existance of what one wants and not anything else as opposed to what one wants and unfortunately gets but can't avoid some extra benifits.

This is one of them. It's plain it'll never be accepted anyway, why the heck shuld AC be abbrupted just when it was waking up, at just that particular moment? Nah!

"Sorry old choice-function, youre TOO OLD..." Sure, that's really convincing. Just about as convincing it is to see arguments against AC and for Countable Choice.

What I'm objecting to is that the silly articles are getting the same attention level as the accepted ones. By that I mean simply that "objections to ZFC" is lowlevel. Even though it happen to be highlevel to these working with it¨¨. —Preceding unsigned comment added by YohanN7 (talkcontribs) 14:57, 21 July 2009 (UTC)

The axiom of dependent choices is not some newly invented and unused thing. On the contrary, it has a long history of being studied by mathematicians. JRSpriggs (talk) 17:34, 21 July 2009 (UTC)
Right — actually DC is a fairly important fragment of choice, one that allows a lot of arguments to go through in real analysis, but doesn't let you wellorder the reals and come up with perceived "pathological" sets of reals. The way to think of it is, DC is what you need to do a transfinite induction of countable length, in which you're allowed to make one choice at each step.
In the very important model L(R), DC is actually true, but AC is not. --Trovatore (talk) 18:31, 21 July 2009 (UTC)
I stand corrected. Are there versions of DC that allow and disallaw Zorns Lemma as well? What I mean is that to me personnally, AC is ok, wellorder is murky, and Zorn is somewhere in between, probably something I want. (Yes, I do know that they are all equivalent under ZF + AC.) By the way, when it comes to paradoxes, there must surely be a few if one introduces NOT AC in the same way that NOT special relativity would yield a host of strange results. Does DC cure that? YohanN7 (talk) 02:02, 22 July 2009 (UTC)
I think you're taking an overly "foundational" approach to DC. I don't know that there are too many folks who are arguing that DC is true but AC is not. The usual view among those who think the question makes sense, is that full AC is true.
But even if you think full AC is true, it's still important to know about DC. Because (oversimplifying here) that's the version of choice you can have in determinacy models. So it's good to know what it can do, what it can't do, and how to reason informally in a context where you can use DC but not AC. --Trovatore (talk) 03:45, 22 July 2009 (UTC)
Yup, your'e right. Besides, I'm here to learn, not to criticize. Iv'e been complaining too much lately;) YohanN7 (talk) 08:37, 22 July 2009 (UTC)