相关论文: A cardinal invariant related to homogeneous famili…

Given a function $f \in \omega^\omega$, a set $A \in [\omega]^\omega$ is free for $f$ if $f[A] \cap A$ is finite. For a class of functions $\Gamma \subseteq \omega^{\omega}$, we define $\mathfrak{ros}_\Gamma$ as the smallest size of a…

A ballean is a set $X$ endowed with some family $\F$ of its subsets, called the balls, in such a way that $(X,\F)$ can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal $\kappa$, we define $\F$…

A group G that is not finitely generated can be written as the union of a chain of proper subgroups. The cofinality spectrum of G, written CF(S), is the set of regular cardinals lambda such that G can be expressed as the union of a chain of…

Let lambda be aleph_0 or a strong limit of cofinality aleph_0. Suppose that (G_m,p_{m,n}:m =< n<omega) and (H_m,p^t_{m,n}: m=< n < omega) are projective systems of groups of cardinality less than lambda and suppose that for every n<omega…

In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $\omega_1$ or $\omega_2$ has small consistency strength, but that of a…

A ``k-rule" is a sequence A=((A_n,B_n):n<omega) of pairwise disjoint sets B_n, each of cardinality at most k, where A_n is a subset of B_n. A set X of natural numbers (a ``real'') follows a rule A if for infinitely many n we have that the…

Let M denote the ideal of first category subsets of R. We prove that min{card X: X \subseteq R, X \not\in M} is the smallest cardinality of a family S \subseteq {0,1}^\omega with the property that for each f: \omega -> \bigcup_{n \in…

A cardinal is weakly Reinhardt if it is the critical point of an elementary embedding from the universe of sets into a model that contains the double powerset of every ordinal. This note establishes the equiconsistency of a proper class of…

In [CMRM24], it was proved that it is relatively consistent that \emph{bounding number} $\mathfrak{b}$ is smaller than the uniformity of $\mathcal{MA}$, where $\mathcal{MA}$ denotes the ideal of the meager-additive sets of $2^{\omega}$. To…

Let $G$ be a finite permutation group acting on a set $\Omega$. An ordered sequence $(\omega_1,\ldots,\omega_\ell)$ of elements of $\Omega$ is an irredundant base for $G$ if the pointwise stabilizer of the sequence is trivial and no point…

Let G be a simple graph with vertex set V(G). A subset S of V(G) is independent if no two vertices from S are adjacent. The graph G is known to be a Konig-Egervary if alpha(G) + mu(G)= |V(G)|, where alpha(G) denotes the size of a maximum…

The magnitude of a graph is one of a family of cardinality-like invariants extending across mathematics; it is a cousin to Euler characteristic and geometric measure. Among its cardinality-like properties are multiplicativity with respect…

We develop a version of Cichon's diagram for cardinal invariants on the generalized Cantor space 2^kappa or the generalized Baire space kappa^kappa where kappa is an uncountable regular cardinal. For strongly inaccessible kappa, many of the…

A homogeneous family of subsets over a given set is one with a very ``rich'' automorphism group. We prove the existence of a bi-universal element in the class of homogeneous families over a given infinite set and give an explicit…

A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex that does not belong to $S$ is adjacent to a vertex in $S$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. The…

In a compact topological dynamical system $(X,f)$, we associate to every pair $(x,y)$ a canonical order-theoretic invariant, its emergent order spectrum $\Omega(x,y)$. We first prove that, if $x$ and $y$ are chain-related, one can always…

The 2-domination number $\gamma_2(G)$ of a graph $G$ is the minimum cardinality of a set $ D \subseteq V(G) $ for which every vertex outside $ D $ is adjacent to at least two vertices in $ D $. Clearly, $ \gamma_2(G) $ cannot be smaller…

We interpret homogenousness as a second order property and base it on the same principle as nonmonotonic logic: there might be a small set of exceptions. We use this idea to analyse fundamental questions about defeasible inheritance…

We consider families of chain-cochain infinite complexes $\mathcal C$ of spaces with elements depending on a number of parameters, and endowed with a converging associative multiple product. The existence of left/right local/non-local…

Starting from a supercompact cardinal we build a model in which $2^{\aleph_{\omega_1}}=2^{\aleph_{\omega_1+1}}=\aleph_{\omega_1+3}$ but there is a jointly universal family of size $\aleph_{\omega_1+2}$ of graphs on $\aleph_{\omega_1+1}$.…