Constructive aspects of models for non-standard analysis

Fredrik Nordvall Forsberg

Research output: Thesis › Master'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

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Nonstandard Analysis
Filter
Ultraproduct
Ultrafilter
Boundedness
Model
Valid
Imply
Theorem

Keywords

  • ultraproducts
  • non standard analysis
  • constructive mathematics

Cite this

Nordvall Forsberg, Fredrik. / Constructive aspects of models for non-standard analysis. 2009. 56 p.
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Nordvall Forsberg, F 2009, 'Constructive aspects of models for non-standard analysis', MPhil, Uppsala University.

Constructive aspects of models for non-standard analysis. / Nordvall Forsberg, Fredrik.

2009. 56 p.

Research output: Thesis › Master's Thesis

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N2 - 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

AB - 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

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KW - non standard analysis

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Nordvall Forsberg F. Constructive aspects of models for non-standard analysis. 2009. 56 p.

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