2000/03/20 by Mirna Džamonja, Saharon Shelah, Džamonja, Mirna +1
Mathematics · #03E05 #03E35 #03E55 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E05 #msc:03E35 #msc:03E55
paper · pdf · doi:10.48550/arxiv.math/0003118
published as J. London Math. Soc. (2) 67 No. 1 (2003) 1--15
arxiv created 2000/03/20 · openalex publication_date 2000/03/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of stationary reflection is one of the most important notions of combinatorial set theory. We investigate weak reflection, which is, as the name suggests, a weak version of stationary reflection. This sort of reflection was introduced in [DjSh:545] (math.LO/9601219), where it was shown that weak reflection has applications to various guessing principles, in the sense that if there is no weak reflection, than a guessing principle holds, and an application dealing with the saturation of normal filters. Further investigations of weak reflection were carried in [CDSh:571] (math.LO/9504221) and [CuSh:596] (math.LO/9703219). While various ZFC restrictions on the one hand, and independence results on the other, were discovered about the weak reflection, the question of the relative consistency of the existence of a regular cardinal kappa such that the first cardinal weakly reflecting at kappa is a successor of singular, remained open. This paper answers that question by proving that (modulo large cardinal assumptions close to 2-hugeness) that there indeed can be such a cardinal kappa.