Constructive aspects of models for non-standard analysis

Research output: ThesisMaster's Thesis

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
Original languageEnglish
QualificationMPhil
Awarding Institution
  • Uppsala University
Publication statusPublished - 2009

Keywords

  • ultraproducts
  • non standard analysis
  • constructive mathematics

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