Very weak metatheories

Timothy Y. Chow tchow at
Thu Jul 28 16:04:56 EDT 2022

Pedro Sanchez Terraf wrote:

> It seems to be a standard practice to use Primitive Recursive Arithmetic 
> as a "finitistic metatheory"; at least that is the take on Kunen's 2011 
> Set Theory book.
> My question, whose greatest sin is to have emerged out of sheer 
> curiosity, is about what happens if one replaces PRA by a weaker, even 
> ultrafinitist, metatheory.
>  * Do relative consistency results (CH, ~CH) go through as usual?
>  * What about the Reflection Principle?
>  * (Your metatheorem of choice)?

A similar question came up on MathOverflow a couple of years ago.  You 
might find some relevant information in the answers and comments.


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