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arXiv · 2407.09630

Calligraphy Concerning Casually Compiled Cardinal Characteristic Comparisons

Thilo Weinert
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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.

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Thilo Weinert. 2026-03-18. Calligraphy Concerning Casually Compiled Cardinal Characteristic Comparisons. https://arxiv.org/abs/2407.09630

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