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Definable well-orders of \(H(\omega _2)\) and GCH. (English) Zbl 1270.03096

Summary: Assuming \(2^{\aleph_0}=\aleph_1\) and \(2^{\aleph_1}=\aleph_2\), we build a partial order that forces the existence of a well-order of \(H(\omega_2)\) lightface definable over \(\langle H(\omega_2), \in\rangle\) and that preserves cardinal exponentiation and cofinalities.

MSC:

03E45 Inner models, including constructibility, ordinal definability, and core models
03E40 Other aspects of forcing and Boolean-valued models
03E50 Continuum hypothesis and Martin’s axiom
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References:

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