相关论文: A stronger form of the theorem constructing a rigi…

Assuming the existence of a strong cardinal $\kappa$ and a measurable cardinal above it, we force a generic extension in which $\kappa$ is a singular strong limit cardinal of any prescribed cofinality, and such that the tree property holds…

The main result is Theorem: Let A be an R-algebra, mu, lambda be cardinals such that |A|<=mu=mu^{aleph_0}<lambda<=2^mu. If A is aleph_0-cotorsion-free or A is countably free, respectively, then there exists an aleph_0-cotorsion-free or a…

Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and a parameter R subseteq H(kappa) such that functions…

We show, assuming PD, that every complete finitely axiomatized second order theory with a countable model is categorical, but that there is, assuming again PD, a complete recursively axiomatized second order theory with a countable model…

A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be the core model. Assume that kappa is a countably closed…

Given a countable group $G$ and two subshifts $X$ and $Y$ over $G$, a continuous, shift-commuting map $\phi : X \to Y$ is called a homomorphism. Our main result states that if every finitely generated subgroup of $G$ has polynomial growth,…

Let $X$ be a compact metric space and let $|A|$ denote the cardinality of a set $A$. We prove that if $f\colon X\to X$ is a homeomorphism and $|X|=\infty$ then for all $\delta>0$ there is $A\subset X$ such that $|A|=4$ and for all $k\in Z$…

Suppose that kappa is a singular cardinal of cofinality omega and GCH holds. Assume that for every n<omega the set of alphas with o(alpha)>= alpha^{+n} is unbounded in kappa.Then there is a cardinal preserving extension satisfying…

We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of…

We show that the tree property, stationary reflection and the failure of approachability at $\kappa^{++}$ are consistent with $\mathfrak{u}(\kappa) = \kappa^+ < 2^\kappa$, where $\kappa$ is a singular strong limit cardinal with the…

We call a bipartite graph {\it homogeneous} if every finite partial automorphism which respects left and right can be extended to a total automorphism. A $(\kappa,{\lambda} )$ bipartite graph is a bipartite graph with left side of size…

We investigate connections between resolvability and different forms of tightness. This study is adjacent to [1,2]. We construct a non-regular refinement $\tau^*$ of the natural topology of the real line $\mathbb{R}$ with properties such…

We describe a framework for proving consistency results about singular cardinals of arbitrary cofinality and their successors. This framework allows the construction of models in which the Singular Cardinals Hypothesis fails at a singular…

For a homomorphism f: A --> B of commutative rings, let D(A,B) denote Ker[Pic(A) --> Pic(B)]. Let k be a field and assume that A is a f.g. k-algebra. We prove a number of finiteness results for D(A,B). Here are four of them. 1: Suppose B is…

A graph is \textit{rigid} if it only admits the identity endomorphism. We show that for every $d\ge 3$ there exist infinitely many mutually rigid $d$-regular graphs of arbitrary odd girth $g\geq 7$. Moreover, we determine the minimum order…

Let B(kappa, lambda) be the subalgebra of P(kappa) generated by [kappa]^{<= lambda}. It is shown that if B is any homomorphic image of B(kappa, lambda) then either |B|< 2^lambda or |B|=|B|^lambda, moreover if X is the Stone space of B then…

An inaccessible cardinal $\kappa$ is supercompact when $(\kappa, \lambda)$-ITP holds for all $\lambda\geq \kappa.$ We prove that if there is a model of $\ZFC$ with two supercompact cardinals, then there is a model of \ZFC where…

For a cardinal $\mathfrak{a}$, let $\mathrm{fin}(\mathfrak{a})$ be the cardinality of the set of all finite subsets of a set which is of cardinality $\mathfrak{a}$. It is proved without the aid of the axiom of choice that for all infinite…

In this article, we characterize the holomorphic mappings from $B_{\ell_p^n}\times\mathbb{D}^{m}$ into $\mathbb{D}^{m}$ for $p\in \{2,\infty\}$. In addition, we give a simple proof for the boundary Schwarz lemma for vector valued…

For an infinite cardinal $\kappa$, let $ded\kappa$ denote the supremum of the number of Dedekind cuts in linear orders of size $\kappa$. It is known that $\kappa<ded\kappa\leq 2^{\kappa}$ for all $\kappa$ and that $ded\kappa<2^{\kappa}$ is…