arXiv subjects

Marc Lischka

Publications and source records attributed to Marc Lischka.

2 recordsLinked to original sources

arXiv2023

More on Halfway New Cardinal Characteristics

We continue investigating variants of the splitting and reaping numbers introduced in arXiv:1808.02442. In particular, answering a question raised there, we prove the consistency of $\mathrm{cof}(\mathcal{M})<\mathfrak{s}_{\frac{1}{2}}$ and of $\mathfrak{r}_{\frac{1}{2}}<\mathrm{add}(\mathcal{M})$. Moreover, we discuss their natural generalisations $\mathfrak{s}_\rho$ and $\mathfrak{r}_\rho$ for $\rho\in (0,1)$, and show that $\mathfrak{r}_\rho$ does not depend on $\rho$.

math.LO↗

arXiv2018

Halfway New Cardinal Characteristics

Based on the well-known cardinal characteristics $\mathfrak{s}$, $\mathfrak{r}$ and $\mathfrak{i}$, we introduce nine related cardinal characteristics by using the notion of asymptotic density to characterise different intersection properties of infinite sets. We prove several bounds and consistency results, e. g. the consistency of $\mathfrak{s} < \mathfrak{s}_{1/2}$, as well as several results about possible values of $\mathfrak{i}_{1/2}$.

math.LO↗