The Universe

[Robert Solovay]

Answers to two of your questions from one One Universe proponent.

1. The true theory of the universe has a transitive set model.

2. As ny theory extending ZFC + V=L is not the theory of the Universe.

Yours sincerely,

Bob Solovay

On Tue, Jul 7, 2020, 9:31 PM Joe Shipman <joeshipman at aol.com> wrote:

> I have been thinking about the debate between the “Multiverse” and “One
> Universe” viewpoints in Set Theory.
>
> It’s a bit hard to figure out exactly what their disagreement is, well
> enough to state what would count as “evidence” for one view or the other.
>
> I’m assuming both camps agree on ZFC, and only count as “Universes” set or
> class models of ZFC which are well-founded, standard, and transitive, to
> sharpen the issues I care about.
>
> I’d also like to ignore distinctions between different models with the
> same theories. So we have exactly continuum-many theories consistently
> extending ZFC. Let S be this set of theories.
>
> Do “One Universe” theorists and “Multiverse” theorists have well-defined
> and opposing views on any statement about which elements of S have standard
> transitive set models or class models?
>
> Do “One Universe” theorists believe that the element of S that is the
> theory of “the” universe has a set model?
>
> Is there any element of S which “One Universe” theorists are sure is not
> the theory of “the” Universe, but which has a standard transitive set or
> class model?
>
> 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?
>
> — JS
>
> Sent from my iPhone
>
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