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BLOWING UP THE POWER OF A SINGULAR CARDINAL OF UNCOUNTABLE COFINALITY
MOTI GITIK
Journal:

The Journal of Symbolic Logic / Volume 84 / Issue 4 / December 2019

Published online by Cambridge University Press:

16 September 2019, pp. 1722-1743

Print publication:

December 2019
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A new method for blowing up the power of a singular cardinal is presented. It allows to blow up the power of a singular in the core model cardinal of uncountable cofinality. The method makes use of overlapping extenders.

SOME APPLICATIONS OF SUPERCOMPACT EXTENDER BASED FORCINGS TO HOD
MOTI GITIK, CARMI MERIMOVICH
Journal:

The Journal of Symbolic Logic / Volume 83 / Issue 2 / June 2018

Published online by Cambridge University Press:

01 August 2018, pp. 461-476

Print publication:

June 2018
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Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V. In particular, a model where all regular uncountable cardinals are measurable in HOD is constructed.

MODIFIED EXTENDER BASED FORCING
DIMA SINAPOVA, SPENCER UNGER
Journal:

The Journal of Symbolic Logic / Volume 81 / Issue 4 / December 2016

Published online by Cambridge University Press:

01 December 2016, pp. 1432-1443

Print publication:

December 2016
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We analyze the modified extender based forcing from Assaf Sharon’s PhD thesis. We show there is a bad scale in the extension and therefore weak square fails. We also present two metatheorems which give a rough characterization of when a diagonal Prikry-type forcing forces the failure of weak square.

A power function with a fixed finite gap everywhere
Carmi Merimovich
Journal:

The Journal of Symbolic Logic / Volume 72 / Issue 2 / June 2007

Published online by Cambridge University Press:

12 March 2014, pp. 361-417

Print publication:

June 2007
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We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2κ = κ+n together with 2λ = λ+n for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible.
When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2λ = λ+n for all cardinals λ.

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