Related papers: Appendix to "Inconsistency of Inaccessibility"
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…
This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018. It provides further details on the language, the complexity results and the datalog translation…
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…
Foreman proved the Duality Theorem, which gives an algebraic characterization of certain ideal quotients in generic extensions. As an application he proved that generic supercompactness of $\omega_1$ is preserved by any proper forcing. We…
We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals…
This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and the failure of various forms of square. These covering…
We prove, via transfinite recursion, the existence, inside any linearly ordered set of appropriate regular cardinality $\lambda$, of a particular kind of well-ordered subsets characterized by the property of $\lambda$-fullness. Let $H$ be a…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
This paper is purely expository. We present short elementary proofs of * the Gauss Theorem on constructibility of regular polygons; * the existence of a cubic equation unsolvable in real radicals; * the existence of a quintic equation…
We study the influence of the existence of large cardinals on the existence of wellorderings of power sets of infinite cardinals $\kappa$ with the property that the collection of all initial segments of the wellordering is definable by a…
According to a theorem due to Kenneth Kunen, under ZFC, there is no ordinal $\lambda$ and non-trivial elementary embedding $j:V_{\lambda+2}\to V_{\lambda+2}$. His proof relied on the Axiom of Choice (AC), and no proof from ZF alone has been…
This article explores the model-dependent nature of set cardinality, emphasizing that cardinality is not absolute but varies across different axiomatic frameworks. Although Cantor's diagonal argument shows the real numbers are…
Motivated by recent results and questions of D. Raghavan and S. Shelah, we present ZFC theorems on the bounding and various almost disjointness numbers, as well as on reaping and dominating families on uncountable, regular cardinals. We…
This document comes as supplementary material of the paper Stability in Gagliardo-Nirenberg inequalities by the same authors. It is intended to state a number of classical or elementary statements concerning constants and inequalities for…
Cicho\'n's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent…
The consistency of a second-order version of a theorem of Morley on the number of countable models was proved in arXiv:2107.07636 with the aid of large cardinals. We here dispense with them.
We introduce reflection properties of cardinals in which the attributes that reflect are expressible by infinitary formulas whose lengths can be strictly larger than the cardinal under consideration. This kind of generalized reflection…
Recent results of Hindman, Leader and Strauss and of Fern\'andez-Bret\'on and Rinot showed that natural versions of Hindman's Theorem fail {\em for all} uncontable cardinals. On the other hand, Komj\'ath proved a result in the positive…
The purpose of this note is to prove irreflexivity, and hence the linear ordering, in ZFC, without some of the machinery used by Dehornoy.
This paper examines the completion of an w-ordered sequence of recursive definitions which on the one hand defines an increasing sequence of nested set and on the other redefines successively a numeric variable as the cardinal of the…