@article{Ferguson_2018, title={Inconsistent Models (and Infinite Models) for Arithmetics with Constructible Falsity}, volume={28}, url={https://apcz.umk.pl/LLP/article/view/LLP.2018.011}, DOI={10.12775/LLP.2018.011}, abstractNote={An earlier paper on formulating arithmetic in a connexive logic ended with a conjecture concerning C♯ , the closure of the Peano axioms in Wansing’s connexive logic C. Namely, the paper conjectured that C♯ is Post consistent relative to Heyting arithmetic, i.e., is nontrivial if Heyting arithmetic is nontrivial. The present paper borrows techniques from relevant logic to demonstrate that C♯ is Post consistent simpliciter, rendering the earlier conjecture redundant. Given the close relationship between C and Nelson’s paraconsistent N4, this also supplements Nelson’s own proof of the Post consistency of N4♯ . Insofar as the present technique allows infinite models, this resolves Nelson’s concern that N4♯ is of interest only to those accepting that there are finitely many natural numbers.}, number={3}, journal={Logic and Logical Philosophy}, author={Ferguson, Thomas Macaulay}, year={2018}, month={Aug.}, pages={389–407} }