Weak reflection at the successor of singular

Mirna Džamonja; Saharon Shelah

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arXiv · math/0003118

Weak reflection at the successor of singular

Mirna Džamonja·Saharon Shelah

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Abstract

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.

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Mirna Džamonja, Saharon Shelah. 2000-03-20. Weak reflection at the successor of singular. https://arxiv.org/abs/math/0003118

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