[FOM] The Universe

[Joe Shipman]

Those axioms don’t seem very well-motivated in that paper. I guess that they sort of say, among other things, that there is no single Universe which contains all the other ones as submodels, but I’m not sure about this.

The most radical “one universe” axiom is the conjunction of V=L and “there is no standard model of ZFC”. If there is a standard model, then this axiom holds in the Cohen/Shepherdson minimal model M, so I like to call the axiom “V=M”. Although the axiom is unsatisfactory in various respects, it certainly shows that there doesn’t have to be a multiverse.

— JS

Sent from my iPhone

> On Jul 9, 2020, at 11:31 PM, Timothy Y. Chow <tchow at math.princeton.edu> wrote:
> 
> Joe Shipman wrote:
> 
>> What is an example of a statement which, if proved in ZFC, might persuade some members of one camp that the other camp was correct?
> 
> The most precise statement of the multiverse view that I know is explained in this article:
> 
> https://arxiv.org/pdf/1104.4450.pdf
> 
> They show that the multiverse axioms are consistent with ZFC.  I don't know if the negations of all these axioms have also been shown to be consistent with ZFC.  If not, perhaps such an axiom would be an answer to your question.
> 
> Tim
>