On a question of Silver about gap-two cardinal transfer principles

摘要

Abstract Assuming the existence of a Mahlo cardinal, we produce a generic extension of G?del’s constructible universe L , in which the $$extit{GCH}$$ GCH holds and the transfer principles $$(leph _2, leph _0) ightarrow (leph _3, leph _1)$$ ( ? 2 , ? 0 ) → ( ? 3 , ? 1 ) and $$(leph _3, leph _1) ightarrow (leph _2, leph _0)$$ ( ? 3 , ? 1 ) → ( ? 2 , ? 0 ) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.