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  1. Preserving levels of projective determinacy by tree forcings.Fabiana Castiblanco & Philipp Schlicht - 2021 - Annals of Pure and Applied Logic 172 (4):102918.
    We prove that various classical tree forcings—for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing—preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes are added to thin projective transitive relations by these forcings.
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  • Full-splitting Miller trees and infinitely often equal reals.Yurii Khomskii & Giorgio Laguzzi - 2017 - Annals of Pure and Applied Logic 168 (8):1491-1506.
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  • Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
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