Etudes in κ-m-proper forcing

Abstract

κ-M-proper forcing, introduced in [K00] when κ = ω1, is a very powerful new technique for generic stepping up, subsuming all previous generic steppings up using auxiliary functions. A general framework for using κ-M-proper forcing is set out, and a couple of examples of such forcings, adding κ−-thin-very tall scattered spaces and long chains in P(κ) modulo <κ−, are given. These objects are not currently obtainable by the previously known techniques.

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