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 (ℵ 2 , ℵ 0) → (ℵ 3 , ℵ 1) and (ℵ 3 , ℵ 1) → (ℵ 2 , ℵ 0) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.
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