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Constructive aspects of models for non-standard analysis

Nordvall Forsberg, Fredrik (2009) Constructive aspects of models for non-standard analysis. Masters thesis, Uppsala University.

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Abstract

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 math- emetics BISH , is also studied. We show that certain theorems in classical mathematics related to reduced prdoucts or non-standard analysis are equiv- alent to or imply BD or LLPO , and thus not constructively provable