2011/09/15 by Damir D. Dzhafarov, Dzhafarov, Damir D., Carl Mummert +1
Computer Science · Mathematics · #03B30 #03E25 (Secondary) #03F35 (Primary) #Advanced Topology and Set Theory #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03B30 #msc:03E25 #msc:03F35
paper · pdf · doi:10.48550/arxiv.1109.3378
This paper corresponds to section 4 of arXiv:1009.3242, "Reverse mathematics and equivalents of the axiom of choice", which has been abbreviated and divided into two pieces for publication
openalex publication_date 2011/09/15 · arxiv created 2012/01/24 · arxiv updated 2012/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the reverse mathematics of the principle stating that, for every property of finite character, every set has a maximal subset satisfying the property. In the context of set theory, this variant of Tukey's lemma is equivalent to the axiom of choice. We study its behavior in the context of second-order arithmetic, where it applies to sets of natural numbers only, and give a full characterization of its strength in terms of the quantifier structure of the formula defining the property. We then study the interaction between properties of finite character and finitary closure operators, and the interaction between these properties and a class of nondeterministic closure operators.