Comment to "Almost disjoint sets, the dense set problem and the partition calculus"
J\'unio Luan Pereira (Independent Researcher)
TL;DR
This paper critiques a proof in Baumgartner's 1976 article on almost disjoint sets and the partition calculus, providing corrections and a stronger related result.
Contribution
It identifies issues in Baumgartner's proof and offers a corrected, more robust proof of a related result.
Findings
Correction of the proof in Baumgartner's article
Presentation of a stronger related theorem
Clarification of issues in the original proof
Abstract
This text highlights issues present in the proof of Lemma 6.10 of the Baumgartner (1943 -- 2011) article "Almost disjoint sets, the dense set problem and the partition calculus" of 1976, and intends to present a correction at the same time it proves a stronger result mentioned in the article to have similar proof.
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Taxonomy
TopicsFunctional Equations Stability Results · Limits and Structures in Graph Theory · Advanced Topology and Set Theory