Related papers: Inaccessibility and Subinaccessibility. In two par…
The work presents the second part of the second edition of its previous one published in 2000 under the same title, containing the proof (in ZF) of the inaccessible cardinals nonexistence, which is enriched and improved now. This part…
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…
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…
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…
This paper is the concise addition to the foregoing work "Inconsistency of Inaccessibility", containing the presentation of main theorem proof (in ZF) about inaccessible cardinals nonexistence. Here some refinement of this presentation is…
This work is a part of my upcoming thesis [7]. We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$-degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2)…
Let $\kappa$ be a regular cardinal, $\lambda<\kappa$ be a smaller infinite cardinal, and $\mathsf K$ be a $\kappa$-accessible category where colimits of $\lambda$-indexed chains exist. We show that various category-theoretic constructions…
We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal.…
We present a survey of some results of the pcf-theory and their applications to cardinal arithmetic. We review basics notions (in section 1), briefly look at history in section 2 (and some personal history in section 3). We present main…
We show that if the existence of a supercompact cardinal $\kappa$ with a weakly compact cardinal $\lambda$ above $\kappa$ is consistent, then the following are consistent as well (where $\mathfrak{t}(\kappa)$ and $\mathfrak{u}(\kappa)$ are…
We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation, then the cardinal was originally…
We extend and improve the result of Makkai and Par\'e that the powerful image of any accessible functor F is accessible, assuming there exists a sufficiently large strongly compact cardinal. We reduce the required large cardinal assumption…
In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(\kappa)\geq2$. In this paper we improve this to $o(\kappa)\geq\kappa+1$ and show that…
This paper contributes to the theory of large cardinals beyond the Kunen inconsistency, or choiceless large cardinal axioms, in the context where the Axiom of Choice is not assumed. The first part of the paper investigates a periodicity…
We show that the existence of a Pi^{1}_{N}-indescribable cardinal over the Zermelo-Fraenkel's set theory ZF is proof-theoretically reducible to iterations of Mostowski collapsings and lower Mahlo operations. Furthermore we describe a…
A well-known version of Rowbottom's theorem for supercompactness ultrafilters leads naturally to notions of two-cardinal Ramseyness and corresponding normal ideals introduced herein. Generalizing results of Baumgartner [7, 8], Feng [22] and…
Our aim is to improve the negative results i.e. non-existence of limit models, and the failure of the generic pair property from math.LO/0609636 to inaccessible lambda as promised there. The motivation is that in [Sh:F756] the positive…
This paper presents results of a survey of authors of journal articles published over several decades in astronomy. The study focuses on determining the characteristics and accessibility of data behind papers, referring to the spectrum of…
A 1984 problem of S.Z. Ditor asks whether there exists a lattice of cardinality aleph two, with zero, in which every principal ideal is finite and every element has at most three lower covers. We prove that the existence of such a lattice…
We provide a model theoretical and tree property like characterization of $\lambda$-$\Pi^1_1$-subcompactness and supercompactness. We explore the behaviour of those combinatorial principles at accessible cardinals.