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arXiv · 1701.00653

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

Mohammad Golshani·Shahram Mohsenipour
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Abstract

Assuming the existence of a Mahlo cardinal, we produce a generic extension of G\"{o}del's constructible universe $L$, in which the transfer principles $(\aleph_2, \aleph_0) \to (\aleph_3, \aleph_1)$ and $(\aleph_3, \aleph_1) \to (\aleph_2, \aleph_0)$ fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.

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Mohammad Golshani, Shahram Mohsenipour. 2017-01-03. On a question of Silver about gap-two cardinal transfer principles. https://arxiv.org/abs/1701.00653

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