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Paper   IPM / M / 16071
School of Mathematics
  Title:   The tree property at the successor of a singular limit of measurable cardinals
  Author(s):  Mohammad Golshani
  Status:   Published
  Journal: Arch. Math. Logic
  Vol.:  57
  Year:  2018
  Pages:   3-25
  Supported by:  IPM
Assume λ is a singular limit of η supercompact cardinals, where η ≤ λ is a limit ordinal. We present two forcing methods for making λ+ the successor of the limit of the first η measurable cardinals while the tree property holding at λ+. The first method is then used to get, from the same assumptions, tree property at ℵη2+1 with the failure of SCH at ℵη2. This extends results of Neeman and Sinapova. The second method is also used to get tree property at successor of an arbitrary singular cardinal, which extends some results of Magidor-Shelah, Neeman and Sinapova.

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