Constructive aspects of models for non-standard analysis

Reduced products are generalizations of ultraproducts where the filter used need not be an ultrafilter. With a suitable choice of filter, we can then get a more constructive model of non-standard analysis. We study properties of such reduced products and investigate what classical results are still valid in a constructive setting. A boundedness principle BD, not derivable in pure constructive mathemetics BISH, is also studied. We show that certain theorems in classical mathematics related to reduced prdoucts or non-standard analysis are equivalent to or imply BD or LLPO, and thus not constructively provable.