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A Constructive Theory of Ordered Sets and their Completions
| Title: | A Constructive Theory of Ordered Sets and their Completions. |
 94 views 36 downloads |
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| Name(s): |
Joseph, Jean S., author Richman, Fred, Thesis advisor Florida Atlantic University, Degree grantor Charles E. Schmidt College of Science Department of Mathematical Sciences |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2018 | |
| Date Issued: | 2018 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 50 p. | |
| Language(s): | English | |
| Abstract/Description: | The context for the development of this work is constructive mathematics without the axiom of countable choice. By constructive mathematics, we mean mathematics done without the law of excluded middle. Our original goal was to give a list of axioms for the real numbers R by only considering the order on R. We instead develop a theory of ordered sets and their completions and a theory of ordered abelian groups. | |
| Identifier: | FA00013007 (IID) | |
| Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2018. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Constructive mathematics Ordered sets Abelian groups |
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| Held by: | Florida Atlantic University Libraries | |
| Sublocation: | Digital Library | |
| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00013007 | |
| Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
