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/