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Paper   IPM / M / 16073
School of Mathematics
  Title:   On a question of Silver about gap-two cardinal transfer principles
1.  Mohammad Golshani
2.  Shahram Mohsenipour
  Status:   Published
  Journal: Arch. Math. Logic
  Vol.:  57
  Year:  2018
  Pages:   27-35
  Supported by:  IPM
Assuming the existence of a Mahlo cardinal, we produce a generic extension of Gödel's constructible universe L, in which the GCH holds and the transfer principles (ℵ2, ℵ0) → (ℵ3, ℵ1) and (ℵ3, ℵ1) → (ℵ2, ℵ0) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.

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