FOM: CH and 2nd-order validity

John Mayberry J.P.Mayberry at
Fri Oct 13 18:54:38 EDT 2000

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

<rbjones at> wrote:

> Is it known whether CH is independent of 2nd-order validity?
> Roger Jones
> RBJones at
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
John Mayberry
School of Mathematics
University of Bristol
J.P.Mayberry at

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