We prove several trichotomy results for ideals of compact sets. Typically, we show that a “sufficiently rich” universally Baire ideal is either Π⁰₃-hard, or Σ⁰₃-hard, or else a σ-ideal.
"Trichotomies for ideals of compact sets." J. Symbolic Logic 71 (2) 586 - 598, June 2006. https://doi.org/10.2178/jsl/1146620160