Re: finiteness

From: carboni@vmimat.mat.unimi.it

... L consists of those ideals T : N---->Omega such that for all n Tn = Inf{Tm | m > n}.

I understand this as saying that n is in the ideal iff every greater m is in the ideal (but I think the inequality m > n has to be non-strict to make sense of this). Hence it's really a filter of N. If that's correct, then my suggestion was wrong. L would be not Idl N, but Idl(N^op). That makes sense regarding dimensions, for if a real vector space is finitely presented using an mxn matrix A (presenting R^n/Im A) then its dimension is n-rank(A), so if rank(A) is in Idl(N), the dimension should be in Idl(N^op). (By the way, what's a full reference for the "Perugia Notes"?) Steve.