The paper establishes the general structure of the inconsistent models of a
rithmetic of [7]. It is shown that such models are constituted by a sequenc
e of nuclei. The nuclei fall into three segments: the first contains improp
er nuclei: the second contains proper nuclei with linear chromosomes: the t
hird contains proper nuclei with cyclical chromosomes. The nuclei have peri
ods which are inherited up the ordering. It is also shown that the improper
nuclei can have the order type of any ordinal. of the rationals. or of any
other order type that can be embedded in the rationals in a certain way.