相关论文: A note on L\"owenheim-Skolem cardinals

We introduce and axiomatize the notion of a reflective cardinal, use it to give semantics to higher order set theory, and explore connections between the notion of reflective cardinals and large cardinal axioms.

We present several results concerning Shelah cardinals.

In this note, we relax the hypothesis of the main results in Kellner-Shelah-T\v{a}nasie's "Another ordering of the ten cardinal characteristics in Cicho\'n's diagram".

The article uses two examples to explore the statement that, contrary to the common wisdom, the properties of singular cardinals are actually more intuitive than those of the regular ones.

In this paper we provide an application to the Neumann problem of a recent three critical points theorem.

Accessible categories admit a purely category-theoretic replacement for cardinality: the internal size. Generalizing results and methods from arXiv:1708.06782, we examine set-theoretic problems related to internal sizes and prove several…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

This paper is intended to survey the basics of localization and anti-localization cardinals on the reals, and its interplay with notions and cardinal characteristics related to measure and category.

For a Tychonoff space $X$, the lattice $\mathscr U_X$ was introduced in L.A. P\'erez-Morales, G. Delgadillo-Pi\~n\'on, and R. Pichardo-Mendoza, "The lattice of uniform topologies on $C(X)$", Questions and Answers in General Topology, 39…

C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam Theorem are considered. Cardinal invariants add, cof, cov and non with respect to meager or nowhere dense subsets are compared. Remarks on invariants cof(nwdY) are…

Two new cardinal functions defined in the class of $n$-Hausdorff and $n$-Urysohn spaces that extend pseudocharacter and closed pseudocharacter respectively are introduced. Through these new functions bounds on the cardinality of $n$-Urysohn…

Galeotti, Khomskii and V\"a\"an\"aanen recently introduced the notion of the upward L\"owenheim-Skolem-Tarski number for a logic, strengthening the classical notion of a Hanf number. A cardinal $\kappa$ is the \emph{upward…

We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.

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…

In this article, we extend some results about algebra $A$ with the group of units $U(A)$ having a special polynomial identity, Laurent polynomial. And we present a new version of B. Hartley Conjecture with these identities.

In [Bon20], model theoretic characterizations of several established large cardinal notions were given. We continue this work, by establishing such characterizations for Woodin cardinals (and variants), various virtual large cardinals, and…

We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.

Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.

These notes provide an introduction to a number of those topics in Classical Mechanics that are useful for field theory.

New cases of the multiplicity conjecture are considered.