Infinite spectra in the first order theory of graphs (Q810048)

The spectrum \(\mathrm{Spec}(A)\) of a sentence \(A\) is, roughly, the set of those \(a\) for which \(A\) has a threshold function at or near \(p=n^a\). Examples are given of \(A\) with infinite spectra and with spectra of order type \(\Omega^i\) for arbitrary \(i\).