Document type
ArticleVersion
Published versionPublication date
Publication license
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/217445
Forcing axioms and the complexity of non-stationary ideals
Journal Title
Authors
Director/Tutor
Journal ISSN
Volume Title
Related resource
Abstract
We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on $\omega_2$ and its restrictions to certain cofinalities. Our main result shows that the strengthening $\mathrm{MM}^{++}$of Martin's Maximum does not decide whether the restriction of the non-stationary ideal on $\omega_2$ to sets of ordinals of countable cofinality is $\Delta_1$-definable by formulas with parameters in $\mathrm{H}\left(\omega_3\right)$. The techniques developed in the proof of this result also allow us to prove analogous results for the full non-stationary ideal on $\omega_2$ and strong forcing axioms that are compatible with CH. Finally, we answer a question of S . Friedman, Wu and Zdomskyy by showing that the $\Delta_1$-definability of the non-stationary ideal on $\omega_2$ is compatible with arbitrary large values of the continuum function at $\omega_2$.
Subject
Subject (English)
Citation
Citation
COX, Sean and LÜCKE, Philipp. Forcing axioms and the complexity of non-stationary ideals. Monatshefte für Mathematik. 2022. Vol. 199, num. 1, pags. 45-84. ISSN 0026-9255. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/217445