Date of Award
2018
Document Type
Dissertation
Publication Status
Version of Record
Submission Date
October 2026
Thesis/Dissertation Advisor [Chair]
Richman, Fred
Abstract
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.
Extent
50 p.
Recommended Citation
Joseph, Jean S., "A Constructive Theory of Ordered Sets and their Completions" (2018). Electronic Theses and Dissertations 2010 - 2019. 1848.
https://digitalcommons.fau.edu/etd_general_6/1848
Identifier
FA00013007
Format
COinS
Comments
Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2018.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.