FOM: Quantifier question

[Fredrik Engström]

Can you express "thereexists at least k things" in that logic? 

Best regards,
Fredrik Engström

friedman at mbi.math.ohio-state.edu wrote:
> 
> Reply to Franzen 7/12/02.
> 
> It appears that the completeness of the axiomatization that you give for "there
> are infinitely many x such that" without function symbols would imply that this
> obeys the compactness theorem. However, even with = as the only semantic
> symbol, it is not compact. E.g., every finite subset of
> 
> therexists at least 2 things
> therexists at least 3 things
> therexists at least 4 things
> ..
> not(therexists infinitely many things)
> 
> is satisfiable, but the whole subset is not.
> 
> Have I misunderstood what you were saying?