A Need (or not) for invoking axiom of choice in a certain case

[martinbn]

Even if it is partly timelike and partly spacelike, it will consists of finitely many pieces on which it is either one or the other.

 

[RockyMarciano]

Even if it is partly timelike and partly spacelike, it will consists of finitely many pieces on which it is either one or the other.

and your point is?

 

[martinbn]

There is no axiom of choice involved.

 

[martinbn]

What is your point in this thread?

 

[RockyMarciano]

There is no axiom of choice involved.

I can see this now, thanks.

What is your point in this thread?

I started the thread trying to convince myself that as I have frequently read the AC is not used in (pseudo)riemannian geometry. I chose an example where my intuition was quite confused and presented it here. Now that this example is clarified and after consulting some advanced books(Hawking&Ellis, Wald) on the field it turns out that there are a few examples(not the one I thought about first and discussed here) where actually the full axiom of choice is needed, not just some amount of it. So I'm a bit crossed with the insistence of many physicists that the AC doesn't come up in physics theories.

 

[martinbn]

And what are those examples?

 

[RockyMarciano]

And what are those examples?

Being just a math aficionado I'm sure I would do a terrible job explaining them(maybe I try in some new thread though), if you take a hold of say Wald just look up "Zorn's lemma" in the index and you are sent to an example dealing with the well-posedness of the initial value problem for the EFE.

 

[martinbn]

That is not related to your questions. The AC is used in the prove of the existence of the maximal Cauchy development, but logicians tell us that it is not needed. The way the prove goes one can prove that there exists a prove without the AC. Noone has given one thought, but we can be sure it exists.

 

[RockyMarciano]

The AC is used in the prove of the existence of the maximal Cauchy development, but logicians tell us that it is not needed. The way the prove goes one can prove that there exists a prove without the AC. Noone has given one thought, but we can be sure it exists.

I see, I would need to know who those logicians are and what they tell us, i.e where do they claim we can be sure such constructive proof exists?, do you have any reference at all or can point me to where I can find it?

 

[WWGD]

I see, I would need to know who those logicians are and what they tell us, i.e where do they claim we can be sure such constructive proof exists?, do you have any reference at all or can point me to where I can find it?

Eye of the Tiger, Marciano. Eye of the Tiger!

 

[martinbn]

I don't have any references or names. I saw the discussion at the end of a talk once.

 

[lavinia]

https://philippelefloch.org/2014/06...al-general-relativity-wednesday-juin-25-2014/

 

[RockyMarciano]

https://philippelefloch.org/2014/06...al-general-relativity-wednesday-juin-25-2014/

I'm aware of this proof, it was published last year. It is quite straightforward for the vacuum equations. There is no rigorous constructive proof yet for the full EFE that I know of, though.
There's also the global geodesics existence requiring the Arzelá-Ascoli theorem which requires the axiom of choice.

 

[RockyMarciano]

I don't have any references or names. I saw the discussion at the end of a talk once.

That's too bad, this site doesn't consider valid such claims without any reference.

 

[RockyMarciano]

Eye of the Tiger, Marciano. Eye of the Tiger!

That was for Balboa, but it's ok. ;)

 

[lavinia]

https://arxiv.org/pdf/0705.3902v3.pdf

 

[RockyMarciano]

https://arxiv.org/pdf/0705.3902v3.pdf

Thanks for the reference but it is pretty useless. It is a bad sign when a ten year old preprint hasn't been published in a peer-reviewed journal. The basic argument the author use to avoid the axiom of choice is to recurr to a choice of three-dimensional geometry and giving up coordinate independence in 4 dimensions.

 

[martinbn]

That's too bad, this site doesn't consider valid such claims without any reference.

Excuse me! Are you trying to be patronizing. Arrogance is something you need to earn.

 

[RockyMarciano]

Excuse me! Are you trying to be patronizing. Arrogance is something you need to earn.

And I guess you think you've earned it.
But no, I'm not. I was just reminding you a rule that I thought that everyone and specially a SA should have in mind.

 

[jim mcnamara]

This thread is closed.