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

Fingerprint

Nonstandard Analysis
Filter
Ultraproduct
Ultrafilter
Boundedness
Model
Valid
Imply
Theorem

Keywords

  • ultraproducts
  • non standard analysis
  • constructive mathematics

Cite this

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title = "Constructive aspects of models for non-standard analysis",
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",
keywords = "ultraproducts, non standard analysis, constructive mathematics",
author = "{Nordvall Forsberg}, Fredrik",
year = "2009",
language = "English",
school = "Uppsala University",

}

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

2009. 56 p.

Research output: ThesisMaster's Thesis

TY - THES

T1 - Constructive aspects of models for non-standard analysis

AU - Nordvall Forsberg, Fredrik

PY - 2009

Y1 - 2009

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

KW - ultraproducts

KW - non standard analysis

KW - constructive mathematics

UR - http://www2.math.uu.se/research/pub/Nordvall_Forsberg1.pdf

M3 - Master's Thesis

ER -