Comparing forcing approaches to dense ideals

Monroe Eskew

Comparing forcing approaches to dense ideals

Logic 2025-03-04 v1

Authors: Monroe Eskew

Abstract

We analyze some posets involved in forcing constructions for dense ideals, showing that the Anonymous Collapse and the Dual Shioya Collapse are equivalent for collapsing a large cardinal to $\omega_2$ . We also give a somewhat simplified construction of a normal ideal $I$ on $\omega_2$ such that $\mathcal{P}(\omega_2)/I \sim \mathrm{Col}(\omega_1,\omega_2)$ .

Keywords

set theory forcing

Cite

@article{arxiv.2503.00964,
  title  = {Comparing forcing approaches to dense ideals},
  author = {Monroe Eskew},
  journal= {arXiv preprint arXiv:2503.00964},
  year   = {2025}
}

Comments

Submitted as part of the proceedings of the meeting, "Recent developments in axiomatic set theory", at the Research Institute for Mathematical Sciences (RIMS), Kyoto University, October 2024

Comparing forcing approaches to dense ideals

Abstract

Keywords

Cite

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