February 8
Sean Cox,
Virginia Commonwealth University
Martin's Maximum and the Diagonal Reflection Principle
Several years ago I introduced the Diagonal Reflection Principle (DRP), a maximal form of simultaneous stationary reflection. Roughly, DRP asserts that for all regular θ≥ω2, there are stationarily many sets W of size ω1 such that every stationary element of W reflects to W (i.e. if S⊂[θ]ω is stationary and S∈W, then S∩[W∩θ]ω is stationary). In that paper I showed that that MM+ω1--even just the '+ω1' version of the forcing axiom for σ-closed forcings--implies DRP. In this talk I will prove that MM, even its technical strengthening MM+ω, does NOT imply DRP, contrary to my initial expectations. This is joint work with Hiroshi Sakai.