Weak reflection at the successor of singular
| dc.creator | Džamonja, Mirna | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2000-03-20 | |
| dc.date.accessioned | 2026-07-07T04:34:22Z | |
| dc.date.available | 2026-07-07T04:34:22Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0003118 | |
| dc.identifier | http://arxiv.org/abs/math/0003118 | |
| dc.identifier | J. London Math. Soc. (2) 67 No. 1 (2003) 1--15 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58873 | |
| dc.subject | Logic | |
| dc.subject | 03E05; 03E35; 03E55 | |
| dc.title | Weak reflection at the successor of singular | |
| dc.type | text |