Stupid Questions Open Thread Round 2

OpenThreadGuy

From Costanza's original thread (entire text):

This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.

Meta:

How often should these be made? I think one every three months is the correct frequency.
Costanza made the original thread, but I am OpenThreadGuy. I am therefore not only entitled but required to post this in his stead. But I got his permission anyway.

From Costanza's original thread (entire text):

This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.

Meta:

How often should these be made? I think one every three months is the correct frequency.
Costanza made the original thread, but I am OpenThreadGuy. I am therefore not only entitled but required to post this in his stead. But I got his permission anyway.

Nope.

ZF is consistent with many negations of strong choice. For example, ZF is consistent with Lebesgue measurability of every subset in R. Well-ordering of R is enought to create unmeasurable set.

So, if ZF could prove existence of such a formula, ZF+measurability would prove contradiction, but ZF+neasurability is equiconsistent with ZF and ZF would be inconsistent.

It is very hard to say anything about any well-ordering of R, they are monster constructions...

Here's a sort of related argument (very much not a math expert here): Any well ordering on the real numbers must be non-computable. If there was a computable order, you could establish a 1-1 correspondence between the natural numbers and the reals (since each real would be emitted on the nth step of the algorithm).

Is that remotely right?

0hairyfigment14y

Upvoted on reflection for the part I quoted, which either answers the question or gives us some reason to distinguish R-in-L (the set we'd call the real numbers if we endorsed the statement "V=L") from "the-real-numbers-as-we-know-them".

2hairyfigment14y

Does a well-ordering on the constructable version of R provably do this? I fear I can't tell if you've addressed my question yet.

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