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Archive for Mathematical Logic

, Volume 57, Issue 1–2, pp 27–35 | Cite as

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

  • Mohammad GolshaniEmail author
  • Shahram Mohsenipour
Article
  • 31 Downloads

Abstract

Assuming the existence of a Mahlo cardinal, we produce a generic extension of Gödel’s constructible universe L, in which the \(\textit{GCH}\) holds and the transfer principles \((\aleph _2, \aleph _0) \rightarrow (\aleph _3, \aleph _1)\) and \((\aleph _3, \aleph _1) \rightarrow (\aleph _2, \aleph _0)\) fail simultaneously. The result answers a question of Silver from 1971. We also extend our result to higher gaps.

Keywords

Cardinal transfer principles Mahlo cardinal Forcing Gödel’s constructible universe 

Mathematics Subject Classification

03E35 03E55 03C55 03C80 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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