Comparing forcing approaches to dense ideals

Monroe Eskew

paper

Comparing forcing approaches to dense ideals

arXiv:2503.00964

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 $I ¨ _{2}$ . We also give a somewhat simplified construction of a normal ideal $I$ on $I ¨ _{2}$ such that $P (I ¨ _{2}) / I \sim Col (I ¨ _{1}, I ¨ _{2})$ .

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