Notes on the κ-presentability of Bousfield localizations of Sp
We first review a general result on the κ-presentability of Bousfield localizations of Sp, along with the ℵ₀-presentability of smashing localizations. We then consider examples of spectra E for which the Bousfield localization Sp_E is (i) non-smashing but ℵ₀-presentable, (ii) not ℵ₀-presentable but dualizable, or (iii) not dualizable but ℵ₁-presentable.