Structure theory of L and its applications

Journal of Symbolic Logic 80 (1):29-55 (2015)
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In this paper, we explore the structure theory ofL under the hypothesisL ⊧ “AD +μis a normal fine measure on” and give some applications. First we show that “ ZFC + there existω2Woodin cardinals”1has the same consistency strength as “ AD +ω1is ℝ-supercompact”. During this process we show that ifL ⊧ AD then in factL ⊧ AD+. Next we prove important properties ofL including Σ1-reflection and the uniqueness ofμinL. Then we give the computation of full HOD inL. Finally, we use Σ1-reflection and ℙmaxforcing to construct a certain ideal on that has the same consistency strength as “ZFC+ there existω2Woodin cardinals.”



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Determinacy from strong compactness of ω1.Nam Trang & Trevor M. Wilson - 2021 - Annals of Pure and Applied Logic 172 (6):102944.

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Determinacy in L.Nam Trang - 2014 - Journal of Mathematical Logic 14 (1):1450006.

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