Mutuverse of Set (Question)

[Lewis]

If number of universe is equal to zfc+ there is an inaccessible cardinal then the size of the mutiverse what will be tier ?

 

[AKUTO123]

Could you explain the question a little more, it's not clear what you mean by this state.

 

[Rakih_Elyan]

If number of universe is equal to zfc+ there is an inaccessible cardinal then the size of the mutiverse what will be tier ?

This is High 1-A at a minimum and likely 0.
Or even higher as they are a cumulative hierarchy.

Hope this helps you even if isn't much
Peace✌

 

[Cat275]

Mutuverse. Anyway I'd imagine it to be as high as high 1-A with many more than inaccessible amount of layers since the universe of sets would already imply the proper class of inaccessible which I know implies a bit different when theres other models as real as it and different views of multiverse but theres that.

Although this probably doesn't answer your question since you are asking about the specific size.

 

[Lewis]

Mutuverse. Anyway I'd imagine it to be as high as high 1-A with many more than inaccessible amount of layers since the universe of sets would already imply the proper class of inaccessible which I know implies a bit different when theres other models as real as it and different views of multiverse but theres that.

Although this probably doesn't answer your question since you are asking about the specific size.

Thank sir . You have helped me again.

 

[Lewis]

This is High 1-A at a minimum and likely 0.
Or even higher as they are a cumulative hierarchy.

Hope this helps you even if isn't much
Peace✌

Thx you

 

[Cat275]

Thank sir . You have helped me again.

 

[Lewis]

I just saw that the thread name was wrong. LOL

 

[Lewis]

Could you explain the question a little more, it's not clear what you mean by this state.

I'm asking about the number of universes in multiverse, it looks like a max tegmark.

 

[Cat275]

I haven't really tried studying the multiverse of sets to an extent where I look at discussions over hamkins or anything like that (haven't done this in a while in general though.) so I can only say it's many and in fact the whole totality of the whole system could be higher than a universe + there exist an inaccessible in size but since all universe are supposed to have ill-founded ideas to other each other universes k is an inaccessible in M1 could possibly not be an inaccessible in M2 and so on however assuming that there is atleast one universe that holds an inaccessible cardinal under zfc + there is a inaccessible cardinal then it should be able to imply the properclass or something similar like a model satisfying properties of various inaccessible cardinals just that you can't exactly say if there is a even stronger universe (there is but this could be the strongest if not specified) which is why I said something akin to a class layers to high 1-A or higher if a certain model or universe can give our cardinal k (for example) a stronger theorem or standard although again every universe is nonstandard to each other so meh and I don't exactly actually know the quantity of the universes so I can't actually directly answer your actual question especially when all I have is zfc + there is an inaccessible cardinal.

This doesn't necessarily mean the multiverse of sets is stronger than the universe of sets though which is ironic but yeah this should give you a idea over things which I'd actually assume you already know these things.

 

[Lewis]

I don't know much about the multiverse of set, but it's easier to overcome the limits of infinity than an apophatic theology that relies solely on god power and I think proper class when applied to Vk in NGB theorem, it is more obvious to define character strength to a level beyond formal system comprehension.

 

[Cat275]

I'm not sure as to why you bringed up apophatic theology but if something is above well-defined definitions then surely it is harder or in fact unable to be defined by definitions and things like what you just said would obviously be easier since it's defined by either strict definitions or lenient ones if you are willing to go risky and use informal objects or ideas. But again I don't think apophatic or the idea of ineffable things or unable to be defined is relevent to the current topic.

 

[Lewis]

I haven't really tried studying the multiverse of sets to an extent where I look at discussions over hamkins or anything like that (haven't done this in a while in general though.) so I can only say it's many and in fact the whole totality of the whole system could be higher than a universe + there exist an inaccessible in size but since all universe are supposed to have ill-founded ideas to other each other universes k is an inaccessible in M1 could possibly not be an inaccessible in M2 and so on however assuming that there is atleast one universe that holds an inaccessible cardinal under zfc + there is a inaccessible cardinal then it should be able to imply the properclass or something similar like a model satisfying properties of various inaccessible cardinals just that you can't exactly say if there is a even stronger universe (there is but this could be the strongest if not specified) which is why I said something akin to a class layers to high 1-A or higher if a certain model or universe can give our cardinal k (for example) a stronger theorem or standard although again every universe is nonstandard to each other so meh and I don't exactly actually know the quantity of the universes so I can't actually directly answer your actual question especially when all I have is zfc + there is an inaccessible cardinal.

This doesn't necessarily mean the multiverse of sets is stronger than the universe of sets though which is ironic but yeah this should give you a idea over things which I'd actually assume you already know these things.

Can you give a clear example that the total number of universes = model M ?

 

[Cat275]

Can you explicitly state that the total number of universes = model m ?

You can't otherwise you just follow a universe of set.

If a certain model m has all the universes then there is an ultimate model that contains all which in this case does not exist in the multiverse idea. All universe are distinc in this case unless if I missed something. (like a specific theorem and I just didn't know.)

Unless if you meant m=77 (for arbitary sake)

And m = the total amount of universe which would make it 77.

 

[Lewis]

. (like a specific theorem and I just didn't know.)

I think you know most about set theory. cat

 

[Cat275]

Btw if you were asking about the M1, M2 thing it's just a way to enumerate the universes and label it in a way that we can make an example that a certain universe follows this standard and the other says this. It's not a specific model that you need to follow however since in the multiverse theory you basically use big big models then them being a model is also valid. Although you can also use other models and just go along the lines of consider the model A a universe or something along those lines, M being a universe is not exactly something you need to follow.

 

[Lewis]

I think this looks similar but is used as the ultimate L.

https://arxiv.org/pdf/2011.14724