English

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

Logic 2017-03-07 v2

Abstract

Assuming the existence of a Mahlo cardinal, we produce a generic extension of G\"{o}del's constructible universe LL, in which the transfer principles (2,0)(3,1)(\aleph_2, \aleph_0) \to (\aleph_3, \aleph_1) and (3,1)(2,0)(\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.

Keywords

Cite

@article{arxiv.1701.00653,
  title  = {On a question of Silver about gap-two cardinal transfer principles},
  author = {Mohammad Golshani and Shahram Mohsenipour},
  journal= {arXiv preprint arXiv:1701.00653},
  year   = {2017}
}