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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

Item type: Thesis (Masters)
ID code: 53291
Keywords: ultraproducts, non standard analysis, constructive mathematics, Mathematics, Logic
Subjects: Science > Mathematics
Department: Faculty of Science > Computer and Information Sciences
Depositing user: Pure Administrator
Date deposited: 05 Jun 2015 09:55
Last modified: 21 Sep 2017 16:29
Related URLs:
URI: https://strathprints.strath.ac.uk/id/eprint/53291
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