ITP, ISP, AND SCH

descriptionPublicationkeyboard_double_arrow_right Article 08 Feb 2019 English Publisher:Cambridge University Press (CUP)Journal:The Journal of Symbolic Logic, volume 84, pages 713-725 (issn: 0022-4812, eissn: 1943-5886,

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Authors: Sherwood Hachtman; Dima Sinapova;

doi: 10.1017/jsl.2019.2

ITP, ISP, AND SCH

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Abstract

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.

Related Organizations

University of Illinois at Urbana Champaign
United States

Keywords

large cardinals, Large cardinals, Prikry forcing, tree property, Consistency and independence results, internal unboundedness

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