Related papers: Even more simple cardinal invariants

Assuming an abstract comparison principle called the Ultrapower Axiom, which is motivated by the comparison process of inner model theory and generalizes the statement that the Mitchell order is linear on normal ultrafilters, we…

We give full characterization of the sequences of regular cardinals that may arise as cardinal sequences of locally compact scattered spaces under GCH. The proofs are based on constructions of universal locally compact scattered spaces.

We introduce a forcing that adds a $\square(\aleph_2,\aleph_0)$-sequence with countable conditions under CH. Assuming the consistency of a weakly compact cardinal, we can find a forcing extension by our new poset in which both…

Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals' uniformity numbers can be pairwise different. In addition we show that, in the…

Starting from large cardinals we construct a pair $V_1\subseteq V_2$ of models of $ZFC$ with the same cardinals and cofinalities such that $GCH$ holds in $V_1$ and fails everywhere in $V_2$.

We study several cardinal characteristics of closed graphs G on compact metrizable spaces. In particular, we address the question when it is consistent for the bounding number to be strictly smaller than the smallest size of a set not…

We prove that the strong polarized relation of $\theta$ above $\omega$ applied simultaneously for every cardinal in the interval $[\aleph_1,\aleph]$ is consistent. We conclude that this positive relation is consistent for every cardinal…

Improving a result of Woodin, we identify some classes of individually consistent but mutually inconsistent generic large cardinal axioms.

We study the general problem of the behaviour of the continuum function in the presence of non-supercompact strongly compact cardinals.

We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal.…

The higher characteristics w_m(G) for a finite abstract simplicial complex G are topological invariants that satisfy k-point Green function identities and can be computed in terms of Euler characteristic in the case of closed manifolds,…

This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and the failure of various forms of square. These covering…

We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal…

Given a forcing notion $P$ that forces certain values to several classical cardinal characteristics of the reals, we show how we can compose $P$ with a collapse (of a cardinal $\lambda>\kappa$ to $\kappa$) such that the composition still…

We study the consistency and consistency strength of various configurations concerning the cardinal characteristics $\mathfrak{s}_\theta,\mathfrak{p}_\theta,\mathfrak{g}_\theta,\mathfrak{r}_\theta,\mathfrak{t}_\theta$ at uncountable regular…

We discuss two general aspects of the theory of cardinal characteristics of the continuum, especially of proofs of inequalities between such characteristics. The first aspect is to express the essential content of these proofs in a way that…

This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.

We discuss how singular can cardinals be in absence of the axiom of choice. We show that, contrasting with known negative consistency results (of Gitik and others), certain positive results are provable. Then we pose some problems.

We provide a model where u(\kappa) < 2^{\kappa} for a supercompact cardinal \kappa. Garti and Shelah have provided a sketch of how to obtain such a model by modifying the construction in a paper of Dzamonja and Shelah; we provide here a…

We will give an overview of four families of cardinal characteristics defined on subspaces $\prod_{\alpha\in\kappa}b(\alpha)$ of the generalised Baire space ${}^\kappa\kappa$, where $\kappa$ is strongly inaccessible and…