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ITP, ISP, AND SCH

Published online by Cambridge University Press:  08 February 2019

SHERWOOD HACHTMAN  and
DIMA SINAPOVA
SHERWOOD HACHTMAN
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT CHICAGO CHICAGO, IL60613, USA E-mail: hachtma1@uic.edu
DIMA SINAPOVA
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND COMPUTER SCIENCE UNIVERSITY OF ILLINOIS AT CHICAGO CHICAGO, IL60613, USA E-mail: sinapova@uic.edu
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Abstract

$ISP$ 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.

Keywords

03E35large cardinalsthe tree propertyinternal unboundednessPrikry forcing
Type
Articles
Information
The Journal of Symbolic Logic , Volume 84 , Issue 2 , June 2019 , pp. 713 - 725
Copyright
Copyright © The Association for Symbolic Logic 2019 

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