On configurations concerning cardinal characteristics at regular cardinals

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Abstract

We study the consistency and consistency strength of various configurations concerning the cardinal characteristics at uncountable regular cardinals. Motivated by a theorem of Raghavan-Shelah who proved that, we explore in the first part of the paper the consistency of inequalities comparing with and. In the second part of the paper we study variations of the extender-based Radin forcing to establish several consistency results concerning from hyper-measurability assumptions, results which were previously known to be consistent only from supercompactness assumptions. In doing so, we answer questions from [1], [15] and [7], and improve the large cardinal strength assumptions for results from [10] and [3].

Original languageAmerican English
Pages (from-to)691-708
Number of pages18
JournalJournal of Symbolic Logic
Volume85
Issue number2
DOIs
StatePublished - Jun 2020

Bibliographical note

Publisher Copyright:
© 2020 Cambridge University Press. All rights reserved.

Keywords

  • consistency strength
  • extender-based Radin forcing
  • groupwise density
  • pseudointersection
  • reaping number
  • splitting number
  • supercompact cardinals

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