What's Tier 0 (Boundless) cardinality.

[OGLimitless]

I've been hearing that Tier 0 is a Mahlo cardinal, but I couldn't find anything on the wiki to confirm this, so I was wondering what cardinality is Tier 0.

From my understanding, here are what the other cardinality of the tiers are:

Low 1-A: ℵ1
1-A: ℵ2
Higher then baseline 1-A: ℵ3 and beyond
High 1-A: Inaccessible Cardinal
Tier 0: Unknown (maybe a Mahlo cardinal)

 

[Kowalski]

Tier 0 baseline should be Mahlo cardinal, as from this thread.

 

[OnsokunoSonic]

So how big is Woodin then? I heard that what makes Manifold (used to be) the strongest tier 0?

 

[Cat275]

So how big is Woodin then? I heard that what makes Manifold (used to be) the strongest tier 0?

Woodin is strictly bigger and stronger than many cardinals strictly bigger and stronger than strong mahlo and strong hyper-mahlo, i should probably explain it more detailed later or some other time, but meh for now im kinda lazy and not bothered at it that much so just giving you an idea on how big it is compared to something like mahlo.

 

[OnsokunoSonic]

Where did you read all of these? I would like to know.

 

[Cat275]

Where did you read all of these? I would like to know.

I use wikipedia but i heard googology is also a good option but i haven't checked it yet and i don't really rely at things like that but you could try checking that out if you want but yeah like i said i use wikipedia.

 

[OnsokunoSonic]

I see. Thanks for the answer.

 

[lordozantr]

I've been hearing that Tier 0 is a Mahlo cardinal, but I couldn't find anything on the wiki to confirm this, so I was wondering what cardinality is Tier 0.

From my understanding, here are what the other cardinality of the tiers are:

Low 1-A: ℵ1
1-A: ℵ2
Higher then baseline 1-A: ℵ3 and beyond
High 1-A: Inaccessible Cardinal
Tier 0: Unknown (maybe a Mahlo cardinal)

mahlo cardinal=baseline 0
weakly compact cardinal=0+
woodin cardinal=0^inf
reinhardt cardinal=0^inf
berkeley cardinal=0^inf

 

[Achille]

mahlo cardinal=baseline 0
weakly compact cardinal=0+
woodin cardinal=0^inf
reinhardt cardinal=0^inf
berkeley cardinal=0^inf

Source?

I don't want to write long posts. That's enough.

 

[Cat275]

It's fine the numbering is just very little compared to the actual layers of the implications and sizes.

I'd argue the second mahlo amount of dimension is the least mahlo amount of layers into 0.

 

[Achille]

It's fine the numbering is just very little compared to the actual layers of the implications and sizes.

I'd argue the second mahlo amount of dimension is the least mahlo amount of layers into 0.

I pretty much agree.

 

[ImmortalDread]

I've been hearing that Tier 0 is a Mahlo cardinal, but I couldn't find anything on the wiki to confirm this, so I was wondering what cardinality is Tier 0.

From my understanding, here are what the other cardinality of the tiers are:

Low 1-A: ℵ1
1-A: ℵ2
Higher then baseline 1-A: ℵ3 and beyond
High 1-A: Inaccessible Cardinal
Tier 0: Unknown (maybe a Mahlo cardinal)

Mahlo Cardinal, but this is not baseline boundless.