[with Robert K. Meyer] “ ‘Strenge’ Arithmetics,” Logique et Analyse 42 (1999) 205–220 (published in 2002).
We consider the virtues of relevant arithmetic couched in the logic E of entailment as opposed to R of relevant implication. The move to a stronger logic allows us to construct a complete system of true arithmetic, in which whenever an entailment A → B is not true (an example: 0=2 → 0=1 is not provable) then its negation ~(A → B) is true.