Doshi, Karan (2021) A Rigorous Procedure for Generating a Well-ordered Set of Reals without use of Axiom of Choice/Well-ordering Theorem. In: Current Topics on Mathematics and Computer Science Vol. 9. B P International, pp. 1-5. ISBN 978-93-91882-90-7
Full text not available from this repository.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.
Item Type: | Book Section |
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Subjects: | Lib Research Guardians > Medical Science |
Depositing User: | Unnamed user with email support@lib.researchguardians.com |
Date Deposited: | 28 Oct 2023 04:37 |
Last Modified: | 28 Oct 2023 04:37 |
URI: | http://journal.edit4journal.com/id/eprint/1972 |