A Formulation of Poincaré's Intuitive Concept of Linear Continuum

Abstract:

      Henri Poincaré's intuitive concept of the linear continuum was described by his famous remark which was noted by Bertrand Russell, and in which the notion of "intimate bond" first appeared. This semi-expository paper gives an exposition of Poincaré's remark, and also aims at a formulation of the intimate bond with the aid of introducing a kind of "leap structure" into Robinson's ^*R as a supplemental construction. As a result, we obtain a kind of hyperstandard model that may be called "Poincaré continuum".