Superatomic Boolean algebras constructed from strongly unbounded functions

Mathematical Logic Quarterly 57 (5):456-469 (2011)

Authors
J. Martinez
Universidad Nacional Autonoma de Mexico
Abstract
Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that κ, λ are infinite cardinals such that κ++ + ≤ λ, κ<κ = κ and 2κ = κ+, and η is an ordinal with κ+ ≤ η < κ++ and cf = κ+. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra equation image such that equation image, equation image for every α < η and equation image. Especially, equation image and equation image can be cardinal sequences of superatomic Boolean algebras
Keywords 54A25  msc201003E35  consistency result  Boolean algebra  54G12  cardinal sequence  locally compact scattered space  06E05  strongly unbounded function  superatomic
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DOI 10.1002/malq.201010014
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References found in this work BETA

PCF Structures of Height Less Than Ω3.Karim Er-Rhaimini & Boban Veličković - 2010 - Journal of Symbolic Logic 75 (4):1231-1248.

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Citations of this work BETA

On Constructions with 2-Cardinals.Piotr Koszmider - 2017 - Archive for Mathematical Logic 56 (7-8):849-876.

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