The consistency of arithmetic revisited

pp. 50-80

in: Yvon Gauthier, Internal logic, Berlin, Springer, 2002

Abstract

Though the Archimedean and my completeness axioms [for Euclidean geometry or the reals respectively], the ordinary continuity axiom is divided into two completely different components. Moreover, with my completeness axiom, not one infinite process is demanded, but we have only a finite number of finite axioms, just as Kronecker demands.