TL;DR
This paper provides a proof within ZF set theory that inaccessible cardinals do not exist, utilizing subinaccessible cardinals, spectra, matrices, and functions to develop the argument.
Contribution
It offers a detailed proof of the nonexistence of inaccessible cardinals in ZF, employing advanced set-theoretic tools and concepts.
Findings
Proof of nonexistence of inaccessible cardinals in ZF
Development of spectra and matrix tools for set theory
Explicit construction and reasoning in set-theoretic hierarchy
Abstract
The work presents the brief exposition of the proof (in ZF) of inaccessible cardinals nonexistence. To this end in view there is used the apparatus of subinaccessible cardinals and its basic tools -- reduced formula spectra and matrices and matrix functions and others. Much attention is devoted to the explicit and substantial development and cultivation of basic ideas, serving as grounds for all main constructions and reasonings
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topology and Set Theory · Mathematical and Theoretical Analysis · Advanced Banach Space Theory