On the -condition |
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| Authors: | Moti Gitik Saharon Shelah |
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| Institution: | (1) Department of Mathematics, California Institute of Technology, 91125 Pasadena, CA, USA;(2) Present address: School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel;(3) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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| 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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