Cantor's Diagonal, Inverse Powerset, and Multilevel Successor Models
Year: 2025
Type: article
Abstract: We present a unified framework showing how Cantor’s diagonal argument can be viewed as a construction of the power set, how one can introduce a partial inverse‐powerset operator P^{-1} into ZFC without inventing new “negative‐rank” sets, and how a tower of countable models (each equipped with a unique nonstandard successor) collapses via P^{-1} to a single “first infinitesimal” successor in the base model. This article collects these ideas into a coherent exposition suitable for readers familiar with basic set theory, model theory, and nonstandard analysis.
Author: harkat, mohamed abdelhakim
Institution: Larbi Ben M'hidi University of Oum El Bouaghi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6930818100
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