English

Calligraphy Concerning Casually Compiled Cardinal Characteristic Comparisons

Logic 2026-03-19 v2 Combinatorics

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 ε\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.

Cite

@article{arxiv.2407.09630,
  title  = {Calligraphy Concerning Casually Compiled Cardinal Characteristic Comparisons},
  author = {Thilo Weinert},
  journal= {arXiv preprint arXiv:2407.09630},
  year   = {2026}
}

Comments

45 pages, two tables, one figure. An error in the proof of Theorem 2.1.7 has been corrected. A few typos were corrected and there are phraseological changes in a few places

R2 v1 2026-06-28T17:39:17.631Z