Title: A Rigorous Procedure for Generating a Well-ordered Set of Reals without use of Axiom of Choice/Well-ordering Theorem
Abstract: Well-ordering of the Reals presents a major challenge in Set theory. Under the standard Zermelo Fraenkel Set theory with the Axiom of Choice (ZFC), a well-ordering of the Reals is indeed possible. However the Axiom of Choice (AC) had to be introduced to the original ZF theory which is then shown equivalent to the well-ordering theorem. Despite the result however, no way has still been found of actually constructing a well-ordered Set of Reals. In this paper the author attempts to generate a well ordered Set of Reals without using the i.e. under theory itself using the Axiom of the Power Set as the guiding principle.
Publication Year: 2021
Publication Date: 2021-08-27
Language: en
Type: book-chapter
Indexed In: ['crossref']
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