Related papers: Indestructibility of compact spaces

In the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $\mathbf{ZF}$, some are shown to be independent of…

The main result of this paper is the proof of the simultaneous consistency, modulo a weakly compact cardinal, of the equality $2^{< \mathfrak{c}} = \mathfrak{c}$ with the following property (*) of partitions of pairs of $\mathfrak{c}$:…

We study the Borel and analytic subsets of the spaces \({}^{\kappa}\kappa\) and \({}^{\kappa}2\) endowed with ideal topologies, where \(\kappa\) is a regular uncountable cardinal. We establish that the Borel hierarchy does not collapse in…

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…

It is shown that, assuming the Continuum Hypothesis, compact Hausdorff space of weight at most $\mathfrak{c}$ is a remainder in a soft compactification of $\mathbb{N}$. We also exhibit an example of a compact space of weight $\aleph_1$ --…

In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which $\aleph_{\omega+1}$ carries a uniform ultrafilter that is $\theta$-indecomposable for every uncountable cardinal $\theta<\aleph_\omega$. In this…

Given a compact space in a fixed universe of set theory, one can naturally define its interpretation in any ZFC extension of the universe. We investigate the stability of some classes of compact spaces with respect to extensions of this…

We prove that if $X$ is a topological space that admits Debreu's classical utility theorem (eg.\ $X$ is separable and connected, second countable, etc.), then order relations on $X$ satisfying milder completeness conditions can be…

We study the complexity of isomorphism of classes of metric structures using methods from infinitary continuous logic. For Borel classes of locally compact structures, we prove that if the equivalence relation of isomorphism is potentially…

The following paper is inspired by Efimov's problem - an undecided problem of whether there exists an infinite compact topological space that does not contain neither non-trivial convergent sequences nor a copy of $\beta\omega$. After…

Answering a question of Usuba, we show that an extendible cardinal can be preserved by a set forcing that is not a small forcing.

We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models where the continuum is aleph_2 in which no such space can have aleph_2 countable levels.

We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q$, $\langle L[P],\in ,P \rangle$ and…

We investigate a combinatorial game on $\omega_1$ and show that mild large cardinal assumptions imply that every normal ideal on $\omega_1$ satisfies a weak version of precipitousness. As an application, we show that that the…

We show that Shelah's Eventual Categoricity Conjecture follows from the existence of class many strongly compact cardinals. This is the first time the consistency of this conjecture has been proven. We do so by showing that every AEC with…

We investigate for which compactifications $\gamma\omega$ of the discrete space of natural numbers $\omega$, the natural copy of the Banach space $c_0$ is complemented in $C(\gamma\omega)$. We show, in particular, that the separability of…

We prove the consistency of $\binom{\mu^+}{\mu}\nrightarrow\binom{\mu^+ \omega_1}{\mu\ \mu}$ where $\mu$ is a strong limit singular cardinal of countable cofinality. This result can be forced at limit of measurable cardinals and at small…

In this note we show that if a continuous-time, nonlinear, time-invariant, finite-dimensional system evolves on a compact subset of Rn and if the Jacobian of the vector field is Hurwitz at each point of the compact set, then there is a…

We prove that on the Baire space $(D^{\kappa},\pi)$, $\kappa \geq \omega_0$ where $D$ is a uniformly discrete space having $\omega _1$-strongly compact cardinal and $\pi$ denotes the product uniformity on $D^\kappa$, there exists a…

Assuming the existence of $\mathfrak c$ incomparable selective ultrafilters, we classify the non-torsion Abelian groups of cardinality $\mathfrak c$ that admit a countably compact group topology. We show that for each $\kappa \in [\mathfrak…