Inconsistent models of arithmetic. II: The general case (Q2710594)

This paper extends the results of Part I [``Inconsistent models of arithmetic. I: Finite models'', J. Philos. Log. 26, 223-235 (1997; Zbl 0878.03017)], to include non-finite cases. Inconsistent models of arithmetic are interpretations of the language of (first-order) arithmetic which model all the truths of the standard model of arithmetic plus more, and which are thereby inconsistent. The models can be chunked into objects called nuclei, and fall into three classes, (i) those with improper nuclei, (ii) those with proper nuclei and linear tails, and (iii) those with proper nuclei and cyclical tails. Improper nuclei may have the order-type of any ordinal and the order-type need not be discrete. The paper concludes with some open questions about inconsistent models of arithmetic.