“School of Mathematics”
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| Paper IPM / M / 16073 |
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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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