Related papers: Cardinal Characteristics and Computability

We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the canonical one. We prove the basic properties of canonical…

We examine topological spaces not distinguishing ideal pointwise and ideal $\sigma$-uniform convergence of sequences of real-valued continuous functions defined on them. For instance, we introduce a purely combinatorial cardinal…

We show how to construct, via forcing, splitting families than are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different,…

Every conditionally convergent series of real numbers has a subseries that diverges. The subseries numbers, previously studied in arXiv:1801.06206 , answer the question how many subsets of the natural numbers are necessary, such that every…

Motivated by a characterization of weakly compact cardinals due to Todorcevic, we introduce a new cardinal characteristic, the C-sequence number, which can be seen as a measure of the compactness of a regular uncountable cardinal. We prove…

In this article, we give a proof for that the cardinality of a function basis of the invariants for a finite dimensional real vector space by a compact group is lower bounded by the intuitive difference of the dimensions of the vector space…

Let $\mathcal{I}$ be an ideal on $\omega$. For $f,g\in\omega^\omega$ we write $f \leq_{\mathcal{I}} g$ if $f(n) \leq g(n)$ for all $n\in\omega\setminus A$ with some $A\in\mathcal{I}$. Moreover, we denote…

We provide a model theoretical and tree property like characterization of $\lambda$-$\Pi^1_1$-subcompactness and supercompactness. We explore the behaviour of those combinatorial principles at accessible cardinals.

It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a…

We develop a new forcing notion for adjoining self-coding cofinitary permutations and use it to show that consistently, the minimal cardinality $\mathfrak a_{\text{g}}$ of a maximal cofinitary group (MCG) is strictly between $\aleph_1$ and…

We show that the notions of generic and Laver-generic supercompactness are first-order definable in the language of ZFC. This also holds for generic and Laver-generic (almost) hugeness as well as for generic versions of other large…

The aim of this article is to define a notion of cardinal utility function called measurable utility and to define it on a connected and separable subset of a weakly ordered topological space. The definition is equivalent to the ones given…

We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and…

There is both theoretical and numerical evidence that the set of irreducible representations of a reductive group over local or finite fields is naturally partitioned into families according to analytic properties of representations.…

This paper provides an extensive study of the $\mathscr{I}$-Miller null ideals $M_\mathscr{I}$, $\sigma$-ideals on the Baire space parametrized by ideals $\mathscr{I}$ on countable sets. These $\sigma$-ideals are associated to the idealized…

The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for…

We consider natural cardinal invariants hm_n and prove several duality theorems, saying roughly: if I is a suitably definable ideal and provably cov(I)>=hm_n, then non(I) is provably small. The proofs integrate the determinacy theory,…

We introduce and study a new type of compactness principle for strong logics that, roughly speaking, infers the consistency of a theory from the consistency of its small fragments in certain outer models of the set-theoretic universe. We…

While there is a well-established notion of what a computable ordinal is, the question which functions on the countable ordinals ought to be computable has received less attention so far. We propose a notion of computability on the space of…

We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…