## 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:

 3e+45 Inner models, including constructibility, ordinal definability, and core models 3e+40 Other aspects of forcing and Boolean-valued models 3e+50 Continuum hypothesis and Martin’s axiom
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### References:

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