Canonical structure in the universe of set theory: part two

We prove a number of consistency results complementary to the ZFC results from our paper [4]. We produce examples of non-tightly stationary mutually stationary sequences, sequences of cardinals on which every sequence of sets is mutually stationary, and mutually stationary sequences not concentrating on a fixed cofinality. We also give an alternative proof for the consistency of the existence of stationarily many non-good points, show that diagonal Prikry forcing preserves certain stationary reflection properties, and study the relationship between some simultaneous reflection principles. Finally we show that the least cardinal where square fails can be the least inaccessible, and show that weak square is incompatible in a strong sense with generic supercompactness.

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: James Cummings, Matthew Foreman, Menachem Magidor
• Keywords: APAL 2006, Certain Stationary Reflection, Simultaneous Reflection Principles, Stationary Sequences