Assuming V = L, for every successor cardinal κ we construct a GCH and cardinal preserving forcing poset ℙ ∈ L such that in the ideal of all non-stationary subsets of κ is Δ₁-definable over H(κ⁺).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-3-2,
author = {Sy-David Friedman and Liuzhen Wu and Lyubomyr Zdomskyy},
title = {D1-Definability of the non-stationary ideal at successor cardinals},
journal = {Fundamenta Mathematicae},
volume = {228},
year = {2015},
pages = {231-254},
zbl = {06414105},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-3-2}
}
Sy-David Friedman; Liuzhen Wu; Lyubomyr Zdomskyy. Δ₁-Definability of the non-stationary ideal at successor cardinals. Fundamenta Mathematicae, Tome 228 (2015) pp. 231-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm229-3-2/