Related papers: A Note on Superamorphous Sets and Dual Dedekind-In…

In this paper, we give a finiteness result on the diffeomorphism types of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric…

Strongly convex sets in Hilbert spaces are characterized by local properties. One quantity which is used for this purpose is a generalization of the modulus of convexity \delta_\Omega of a set \Omega. We also show that \lim_{\epsilon \to 0}…

We prove the automorphism conjecture for ordered sets of width less than or equal to 11. The proof supports the meta conjecture that a large number of automorphisms is achievable only as some type of product of independent automorphisms on…

A local description of the non-flat infinitesimally bendable Euclidean hypersurfaces was recently given by Dajczer and Vlachos \cite{DaVl}. From their classification, it follows that there is an abundance of infinitesimally bendable…

Let $G$ be a residually finite group and let $A$ be a finite set. We prove that if $X \subset A^G$ is a strongly irreducible subshift of finite type containing a periodic configuration then periodic configurations are dense in $X$. The…

We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]

Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing the idea of interaction among all parts of a given definable…

We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds with universal cover a bounded domain is a finite set.

A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many…

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to…

In the several contexts such as combinatorial number theory, families of sets of positive integers closed under taking subsets have been investigated. Then it is sometimes useful to give bijections between the set of the one-sided infinite…

We prove that, consistently, there exists a weakly but not strongly inaccessible cardinal $\lambda$ for which the sequence $\langle 2^\theta:\theta<\lambda\rangle$ is not eventually constant and the weak diamond fails at $\lambda$. We also…

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it has countably many complete 1-types over every finite subset of G. We show here…

Let $A$ be a finite ordered set. Define the ordered set $A^A$ as the set of all maps from $A$ to $A$, ordered pointwise. Let ${}^{A} A$ be the dual of $A^A$. We prove results in the spirit of Parts~I--III, but now using both $A^A$ and…

Let "ex" be the cardinality of the smallest independent family of subsets of omega (independent means that all nontrivial Boolean combinations are infinite) which cannot be extended to a homogeneous independent family. "Homogeneous" means…

Extension dimension is characterized in terms of $\omega$-maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some…

A poset is representable if it can be embedded in a field of sets in such a way that existing finite meets and joins become intersections and unions respectively (we say finite meets and joins are preserved). More generally, for cardinals…

Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…

One says that a pair of sets $(S,Q)$ in $\mathbb{R}$ is 'annihilating' if no function can be concentrated on $S$ while having its Fourier transform concentrated on $Q$. One uses to distinguish between weak and strong annihilation types. It…