Inaccessibility and subinaccessibility. In two parts. Part II (in Russian)

TL;DR

This paper provides a detailed proof within ZF set theory that inaccessible cardinals do not exist, utilizing advanced tools like reduced formula spectra and matrices, with applications and implications for set theory and logic.

Contribution

It offers a refined, transparent proof of inaccessible cardinal nonexistence using subinaccessible cardinals and related tools, expanding on previous work by Alexander Kiselev.

Findings

Proof of nonexistence of inaccessible cardinals in ZF

Development of theories of reduced formula spectra and matrices

Implications for set theory and mathematical logic

Abstract

This work represents a translation from English into Russian of the second part of the monograph by Alexander Kiselev under the same title. It contains the proof (in ZF) of inaccessible cardinals nonexistence. The first edition of this work was published in 2000. This part II contains applications of the subinaccessible cardinals apparatus and its basic tools - theories of reduced formula spectra and matrices, disseminators and others, which are used here in this proof and are set forth now in their more transparent and refined form. Much attention is devoted to the more explicit and substantial development and cultivation of basic ideas, serving as grounds for all main constructions and reasonings. The proof of the theorem about inaccessible cardinals nonexistence is presented in its detailed exposition. Several easy consequences of this theorem and some well-known results are presented. Appropriated for specialists in Set Theory and Mathematical Logic, and also for teachers and students of faculties of the mathematical profile.