Related papers: On Gaps under GCH Type Assumptions

The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.

Relative to class many supercompact cardinals, we construct a model of $\ZFC+\GCH$ where for every singular cardinal $\delta$ of countable cofinality and every regular uncountable $\mu<\delta$ there are stationarily many non-approachable…

The aim of this note is to study the convergence in capacity for functions in the class $\mathcal E(X,\omega)$. We obtain several stability theorems. Some of these are (optimal) generalizations of results of Xing, while others are new.

In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…

The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is injective (a weakening of the generalized continuum…

This proof of Godel's first incompleteness theorem doesn't require omega-consistency, nor does it refer to codes of negated sentences as in Rosser's. It begins from where Godel's usual proof ends, and stalks it till it ends proving it.

Continuing [Fuchino, Ottenbreit and Sakai[9, 10]] and [Fuchino and Ottenbreit[11]], we further study reflection principles in connection with the L\"owenheim-Skolem Theorems of stationary logics. In this paper, we mainly analyze the…

Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcing axiom PFA implies these principles…

In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…

Let $B$ be a smooth projective curve of genus $g$, and $S \subset B$ be a finite subset of cardinality $s$. We give an effective upper bound on the number of deformation types of admissible families of canonically polarized manifolds of…

I review the state of the art of the investigation on the structure formation in $f(R)$-gravity based on the Covariant and Gauge Invariant approach to perturbations. A critical analysis of the results, in particular the presence of…

In this paper, which is a sequel to math.DG/9902111, we analyze the limit of the p-form Laplacian under a collapse with bounded sectional curvature and bounded diameter to a singular limit space. As applications, we give results about upper…

We prove a result on the singularities of ball quotients $\Gamma\backslash\CC H^n$. More precisely, we show that a ball quotient has canonical singularities under certain restrictions on the dimension $n$ and the underlying lattice. We also…

Let $M$ denote the Merimovich's model in which for each infinite cardinal $\lambda, 2^\lambda=\lambda^{+3}$. We show that in $M$ the following hold: (1) Shelah's strong hypothesis fails at all singular cardinals, indeed, $\forall \lambda…

We study the generalized dominating number $\mathfrak{d}_{\mu}$ at a singular cardinal $\mu$ of cofinality $\kappa$. We show two lower bounds: in ZFC, $\mathrm{cf}([\mu]^\kappa,\subseteq) \leq \mathfrak{d}_{\mu}$, and under mild…

This is the second part of a work initiated in \cite{GaHa}, where we constructed a model category, $\Qt$, for set theory. In the present paper we use this model category to introduce homotopy-theoretic intuitions to set theory. Our main…

Given a strong limit cardinal $\lambda$ of countable cofinality, we show that if every $\lambda$-coanalytic subset of the generalised Cantor space ${}^{\lambda}2$ has the $\lambda$-$\mathsf{PSP}$, then there is an inner model with…

Let G be a powerful finite p-group. In this note, we give a short elementary proof of the following facts for all $i\ge 0$: (i) $\exp \Omega_-i(G)\le p^i$ for odd p, and $\exp \Omega_-i(G)\le 2^{i+1}$ for p = 2; (ii) the index $|G:G^{p^i}|$…

Let T be the family of open subsets of a topological space (not necessarily Hausdorff or even T_0). We prove that if T has a base of cardinality <= mu, lambda <= mu < 2^lambda, lambda strong limit of cofinality aleph_0, then T has…

Let K be an abstract elementary class satisfying the joint embedding and the amalgamation properties. Let m be a cardinal above the the L\"owenheim-Skolem number of the class. Suppose K satisfies the disjoint amalgamation property for limit…