In Set theory, well-ordering of the Reals is a major difficulty. A well-ordering of the Reals is achievable under conventional Zermelo Fraenkel Set theory with the Axiom of Choice (ZFC). The Axiom of Choice (AC) had to be added to the original ZF theory before it could be demonstrated to be equal to the well-ordering theorem. Regardless of the outcome, no method for really generating a well-ordered Set of Reals has been discovered. The author of this paper aims to build a well-ordered Set of Reals without using the axiom of the Power Set as the driving principle, i.e. under theory itself.
Author (S) Details
Karan Doshi
Chemical Engineering, University of Mumbai, Mumbai, India and Chemical Engineering, Texas Tech University, Lubbock, Texas, USA.
View Book :- https://stm.bookpi.org/CTMCS-V9/article/view/3633
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