2012/01/13 by Justin Palumbo, Palumbo, Justin · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Computer science #Conjecture #Discrete mathematics #Extension (predicate logic) #FOS: Mathematics #Infinity #Logic (math.LO) #Mathematical analysis #Mathematics #Microtubule and mitosis dynamics #Monotonic function #Representation (politics) #Representation theorem #math.LO
paper · pdf · doi:10.48550/arxiv.1201.2932
17 pages
arxiv created 2012/01/13 · openalex publication_date 2012/01/13 · arxiv updated 2012/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We give results exploring the relationship between dominating and unbounded reals in Hechler extensions, as well as the relationships among the extensions themselves. We show that in the standard Hechler extension there is an unbounded real which is dominated by every dominating real, but that this fails to hold in the tree Hechler extension. We prove a representation theorem for dominating reals in the standard Hechler extension: every dominating real eventually dominates a sandwich composition of the Hechler real with two ground model reals that monotonically converge to infinity. We apply our results to negatively settle a conjecture of Brendle and Löwe. We also answer a question due to Laflamme.