Geodesic
A classification of definable forcings on ω1
Fundamenta Mathematicae, Tome 153 (1997) no. 2, pp. 141-144

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Under the assumption of the existence of sharps for reals all simply definable posets on $ω_1$ are classified up to forcing equivalence. 
Jindřich Zpletal. A classification of definable forcings on ω1. Fundamenta Mathematicae, Tome 153 (1997) no. 2, pp. 141-144. doi: 10.4064/fm-153-2-141-144
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