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1 results

ITP, ISP, AND SCH
SHERWOOD HACHTMAN, DIMA SINAPOVA
Journal:

The Journal of Symbolic Logic / Volume 84 / Issue 2 / June 2019

Published online by Cambridge University Press:

08 February 2019, pp. 713-725

Print publication:

June 2019
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$ISP$ cannot hold at the first or second successor of a singular strong limit of countable cofinality; on the other hand, we force a failure of “strong ${\rm{SCH}}$” across a cardinal where $ITP$ holds. We also show that $ITP$ does not imply that there are stationary many internally unbounded models.