Calligraphy Concerning Casually Compiled Cardinal Characteristic Comparisons

TL;DR

This paper explores relationships between various cardinal characteristics of the continuum, establishing inequalities and contextualizing these results within a broader mathematical framework.

Contribution

It introduces new inequalities among cardinal characteristics and provides a comprehensive diagram and historical context for these relationships.

Findings

Partition splitting number is not larger than the uniformity of the meagre ideal.

Not all sets of reals with the cardinality of the ε-almost bisecting number are of strong measure zero.

Fewer sets of strong measure zero than the statistically reaping number are needed to cover the reals.

Abstract

The paper establishes several inequalities between cardinal characteristics of the continuum. In particular, it is shown that the partition splitting number is not larger than the uniformity of the meagre ideal; not all sets of reals having the cardinality of an the $\varepsilon$-almost bisecting number are of strong measure zero; no fewer sets of strong measure zero than indicated by the statistically reaping number suffice to cover the reals; the pair-splitting number is not smaller than the evasion number; and the subseries number is neither smaller than the pair-splitting number nor than the minimum of the unbounding number and the unbisecting number. Moreover, a diagram putting these results into context is provided and a brief historical account is given.