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

TL;DR

This paper provides a Russian translation of the first part of Kiselev's monograph, detailing the proof of the nonexistence of inaccessible cardinals using advanced set-theoretic tools, aimed at specialists and students.

Contribution

It offers a detailed, transparent presentation of the apparatus of subinaccessible cardinals and the proof of their nonexistence within ZF set theory, enhancing understanding of these concepts.

Findings

Proof of nonexistence of inaccessible cardinals in ZF

Development of theories of reduced formula spectra and matrices

Explicit presentation of subinaccessible cardinals and related tools

Abstract

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