FOM: CH and 2nd-order validity

[John Mayberry]

On Fri, 13 Oct 2000 13:33:17 +0100 Roger Bishop Jones 

<rbjones at rbjones.com> wrote:

> Is it known whether CH is independent of 2nd-order validity?
> 
> Roger Jones
> RBJones at RBJones.com
> 
> 
Dear Roger,
It's not entirely clear what you mean by the question, but since all 
complete ordered fields are isomorphic, either CH holds in all models 
of the second order theory of complete ordered fields (the axiomatic 
theory of the reals) or its negation holds in all such models. In 
that sense it is not independent of second order validity.

John Mayberry
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John Mayberry
School of Mathematics
University of Bristol
J.P.Mayberry at Bristol.ac.uk
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