Abstract
In [5], XI, S. Shelah formulated a condition on forcing notion ( -condition) which implies that the forcing it satisfies does not add reals. It was proved that, under some additional demands, this condition is preserved by revised countable support iterations. We are going to show that these demands can be weakened. A few examples of simple forcing notions that can iterate while preserving the-condition, and hence without adding reals, are presented.
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Gitik, M., Shelah, S. On the -condition. Israel J. Math. 48, 148–158 (1984). https://doi.org/10.1007/BF02761160
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DOI: https://doi.org/10.1007/BF02761160