Dissertation/Thesis Abstract

A Constructive Theory of Ordered Sets and Their Completions
by Joseph, Jean S., Ph.D., Florida Atlantic University, 2018, 50; 10807924
Abstract (Summary)

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.

Indexing (document details)
Advisor: Richman, Fred, Klingler, Lee
Commitee: Lubarsky, Robert, Zhang, Xiao-Dong
School: Florida Atlantic University
Department: Mathematics
School Location: United States -- Florida
Source: DAI-B 79/10(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Completions, Constructive mathematics, Ordered abelian groups, Ordered sets
Publication Number: 10807924
ISBN: 9780438012554
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