The Journal of Symbolic Logic

Research Article

Inconsistent models of arithmetic Part II: the general case

Graham Priest

Department of Philosophy, University of Queensland, Brisbane, Australia, 4072, E-mail:


The paper establishes the general structure of the inconsistent models of arithmetic of [7]. It is shown that such models are constituted by a sequence of nuclei. The nuclei fall into three segments: the first contains improper nuclei: the second contains proper nuclei with linear chromosomes: the third contains proper nuclei with cyclical chromosomes. The nuclei have periods 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.

(Received May 30 1997)

(Revised November 16 1998)