Thin equivalence relations in scaled pointclasses |
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| Authors: | Ralf Schindler Philipp Schlicht |
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| Affiliation: | 1. Institut für mathematische Logik und Grundlagenforschung, Westf?lische Wilhelms‐Universit?t Münster, Einsteinstra?e 62, 48149 Münster, Germany;2. Mathematisches Institut, Rheinische Friedrich‐Wilhelms‐Universit?t Bonn, Endenicher Allee 60, 53115 Bonn, Germany |
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| Abstract: | For ordinals α beginning a Σ1 gap in $mathrm{L}(mathbb {R})$, where $Sigma _{1}^{mathrm{J}_{alpha }(mathbb {R})}$ is closed under number quantification, we give an inner model‐theoretic proof that every thin $Sigma _{1}^{mathrm{J}_{alpha }(mathbb {R})}$ equivalence relation is $Delta _{1}^{mathrm{J}_{alpha }(mathbb {R})}$ in a real parameter from the (optimal) hypothesis $mathsf {AD}^{mathrm{J}_{alpha }(mathbb {R})}$. |
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| Keywords: | Thin equivalence relations scaled pointclasses term capturing MSC (2010) 03E15 03E45 |
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