A note on Brouwer's weak continuity principle and the transfer principle in nonstandard analysis

A well-known model of nonstandard analysis is obtained by extending the structure of real numbers using an ultra power construction. A constructive approach due to Schmieden and Laugwitz uses instead a reduced power construction modulo a cofinite filter, but has the drawback that the transfer principle is weak. In this paper it is shown that this principle can be strengthened by employing Brouwerian continuity axioms familiar from intuitionistic systems. We end by commenting on the relation between the transfer principle and Ishihara’s boundedness principle.