THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL

James Cummings, Yair Hayut, Menachem Magidor, Itay Neeman, Dima Sinapova, Spencer Unger

Research output: Contribution to journalArticlepeer-review

Abstract

We present an alternative proof that from large cardinals, we can force the tree property at κ+ and κ++ simultaneously for a singular strong limit cardinal κ. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for κ = ℵω2.

Original languageAmerican English
Pages (from-to)600-608
Number of pages9
JournalJournal of Symbolic Logic
Volume86
Issue number2
DOIs
StatePublished - 1 Jun 2021

Bibliographical note

Publisher Copyright:
© 2020, Association for Symbolic Logic

Keywords

  • forcing
  • singular cardinal
  • tree property

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