FOM: CH and 2nd-order validity

Robert Black Robert.Black at
Fri Oct 13 12:41:35 EDT 2000

>Is it known whether CH is independent of 2nd-order validity?
>Roger Jones
>RBJones at

I'm not quite sure what this means, since after 'independent of' I expect
the name of a statement or set of axioms, but obviously *if* we can make
absolute sense of second-order validity/entialment ('absolute' here meaning
not just relative to particular first-order set-theoretical axioms) then CH
is true iff entailed by the axioms of second-order ZF, i.e. iff the
conditional whose antecedent is the conjunction of those (finitely many!)
axioms and whose consequent is CH is second-order valid.

[Of course this provides no programme whatsoever for determining the
truth-value of CH.]


Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

tel. 0115-951 5845

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