A model for a very good scale and a bad scale

Journal of Symbolic Logic 73 (4):1361-1372 (2008)
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Abstract

Given a supercompact cardinal κ and a regular cardinal Λ < κ, we describe a type of forcing such that in the generic extension the cofinality of κ is Λ, there is a very good scale at κ, a bad scale at κ, and SCH at κ fails. When creating our model we have great freedom in assigning the value of 2κ, and so we can make SCH hold or fail arbitrarily badly

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10.2178/jsl/1230396925

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Citations of this work

Aronszajn trees and failure of the singular cardinal hypothesis.Itay Neeman - 2009 - Journal of Mathematical Logic 9 (1):139-157.
Diagonal Prikry extensions.James Cummings & Matthew Foreman - 2010 - Journal of Symbolic Logic 75 (4):1383-1402.
The tree property and the failure of SCH at uncountable cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
Another method for constructing models of not approachability and not SCH.Moti Gitik - 2021 - Archive for Mathematical Logic 60 (3):469-475.

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References found in this work

Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (01):35-98.
Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.

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