On the connection between Nonstandard Analysis and Constructive Analysis
- Author
- Sam Sanders (UGent)
- Organization
- Abstract
- Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.
- Keywords
- Reuniting the antipodes, Nonstandard Analysis, Models of computation, Omega-invariance, Constructive Analysis
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-3099830
- MLA
- Sanders, Sam. “On the Connection between Nonstandard Analysis and Constructive Analysis.” LOGIQUE ET ANALYSE, vol. 222, 2013, pp. 183–210.
- APA
- Sanders, S. (2013). On the connection between Nonstandard Analysis and Constructive Analysis. LOGIQUE ET ANALYSE, 222, 183–210.
- Chicago author-date
- Sanders, Sam. 2013. “On the Connection between Nonstandard Analysis and Constructive Analysis.” LOGIQUE ET ANALYSE 222: 183–210.
- Chicago author-date (all authors)
- Sanders, Sam. 2013. “On the Connection between Nonstandard Analysis and Constructive Analysis.” LOGIQUE ET ANALYSE 222: 183–210.
- Vancouver
- 1.Sanders S. On the connection between Nonstandard Analysis and Constructive Analysis. LOGIQUE ET ANALYSE. 2013;222:183–210.
- IEEE
- [1]S. Sanders, “On the connection between Nonstandard Analysis and Constructive Analysis,” LOGIQUE ET ANALYSE, vol. 222, pp. 183–210, 2013.
@article{3099830,
abstract = {{Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.}},
author = {{Sanders, Sam}},
issn = {{0024-5836}},
journal = {{LOGIQUE ET ANALYSE}},
keywords = {{Reuniting the antipodes,Nonstandard Analysis,Models of computation,Omega-invariance,Constructive Analysis}},
language = {{eng}},
pages = {{183--210}},
title = {{On the connection between Nonstandard Analysis and Constructive Analysis}},
volume = {{222}},
year = {{2013}},
}