2023/04/15 by Jorge Antonio Cruz Chapital, Chapital, Jorge Antonio Cruz, Osvaldo Guzmán +3
Computer Science · Mathematics · Psychology · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Philosophy and Theoretical Science
paper · pdf · doi:10.48550/arxiv.2304.07624
openalex publication_date 2023/04/15 · openalex created_date 2023/04/20 · openalex updated_date 2026/07/28
A structural analysis of construction schemes is developed. That analysis is used to give simple and new constructions of combinatorial objects which have been of interest to set theorists and topologists. We then continue the study of capturing axioms associated to construction schemes. From them, we deduce the existence of several uncountable structures which are known to be independent from the usual axioms of Set Theory. Lastly, we prove that the capturing axiom FCA(part) is implied by Jensen's \Diamond principle.