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 by only considering the order on the real numbers. We instead develop a theory of ordered sets and their completions and a theory of ordered abelian groups.
|Advisor:||Richman, Fred, Klingler, Lee|
|Commitee:||Lubarsky, Robert, Zhang, Xiao-Dong|
|School:||Florida Atlantic University|
|School Location:||United States -- Florida|
|Source:||DAI-B 79/10(E), Dissertation Abstracts International|
|Keywords:||Completions, Constructive mathematics, Ordered abelian groups, Ordered sets|
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