Vladimir_Nesov comments on Contrived infinite-torture scenarios: July 2010 - Less Wrong

24 Post author: PlaidX 23 July 2010 11:54PM

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Comment author: Vladimir_Nesov 31 July 2010 12:14:14AM 0 points [-]

No, because there's an uncountable infinity of uncountable infinities.

The class of all uncountable infinities is not a set, so it can't be an uncountable infinity.

Comment author: Sniffnoy 03 August 2010 05:00:13AM 0 points [-]

This seems a bad way to think about things - except maybe for someone who's just been introduced to formal set theory - especially as proper classes are precisely those classes that are too big to be sets.

Comment author: Larks 31 July 2010 12:32:40AM 0 points [-]

Doesn't the countable-uncountable distinction, or something similar, apply for proper classes?

Comment author: Sniffnoy 03 August 2010 05:00:37AM 0 points [-]

As it turns out, proper classes are actually all the same size, larger than any set.

Comment author: Larks 04 August 2010 12:12:35PM 0 points [-]

Thanks for the correction :)

Comment author: Douglas_Knight 03 August 2010 05:17:31AM 0 points [-]

No. For example, the power set of a proper class is another proper class that is bigger.

Comment author: Sniffnoy 03 August 2010 05:19:49AM 0 points [-]

No, the power set (power class?) of a proper class doesn't exist. Well, assuming we're talking about NBG set theory - what did you have in mind?

Comment author: Douglas_Knight 03 August 2010 05:43:55AM 0 points [-]

oops...I was confusing NBG with MK.

Comment author: Sniffnoy 03 August 2010 06:57:05AM 0 points [-]

M, I don't know anything about MK.

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