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A Constructive Theory of Ordered Sets and their Completions

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Date Issued:
2018
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.
Title: A Constructive Theory of Ordered Sets and their Completions.
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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
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
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/
Owner Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.