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On the one hand, we have seen that every forcing notion which adds dominating reals also adds splitting reals (see FACT 21.0). On the other hand, we have seen in Chapter 22 that Cohen forcing is a forcing notion which adds splitting reals, but which does not add dominating reals.

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Silver-Like Forcing Notions

  • 章节

  • 发表日期：

    2025年

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  • Lorenz J. Halbeisen

摘要

On the one hand, we have seen that every forcing notion which adds dominating reals also adds splitting reals (see FACT 21.0). On the other hand, we have seen in Chapter 22 that Cohen forcing is a forcing notion which adds splitting reals, but which does not add dominating reals.