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“School of Mathematics”

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Paper   IPM / M / 16079
School of Mathematics
  Title:   An Easton like theorem in the presence of Shelah cardinals
  Author(s):  Mohammad Golshani
  Status:   Published
  Journal: Arch. Math. Logic
  Vol.:  56
  Year:  2017
  Pages:   273-287
  Supported by:  IPM
  Abstract:
We show that Shelah cardinals are preserved under the canonical
GCH
GCH forcing notion. We also show that if
GCH
GCH holds and
F:REGCARD
F:REGźCARD is an Easton function which satisfies some weak properties, then there exists a cofinality preserving generic extension of the universe which preserves Shelah cardinals and satisfies
∀κ ∈ REG,  2κ=F(κ)
źźźREG,2ź=F(ź). This gives a partial answer to a question asked by Cody (Arch Math Logic 52(5-6):569-591, 2013) and independently by Honzik (Acta Univ Carol 1:55-72, 2015). We also prove an indestructibility result for Shelah cardinals.

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