2023/11/21 by Aguilera, Juan P., Switzer, Corey Bacal
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2311.12533
We study the question of when a given countable ordinal α is Σ1n- or Π1n-reflecting in models which are neither PD models nor the constructible universe, focusing on generic extensions of L. We prove, amongst other things, that adding any number of Cohen or random reals, or forcing with Sacks forcing or any lightface Borel weakly homogeneous ccc forcing notion cannot change such reflection properties. Moreover we show that collapse forcing increases the value of the least reflecting ordinals but, curiously, to ordinals which are still smaller than the ω1 of L.