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arXiv · 2402.00144

Soft-linkedness

Miguel A. Cardona
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Abstract

We have revised the softness property introduced by J\"org Brendle and Haim Judah (perfect sets of random reals. Israel J. Math., 83(1-2):153-176, 1993), to present a new definition of a class of posets called $\sigma$-soft-linked. Our work demonstrates that these posets work well to preserve the evasion number as well as the bounding number small in generic extensions. Furthermore, we establish a connection between our concept and the Fr\'echet-linked notion introduced by Diego A. Mej\'ia (Matrix iterations with vertical support restrictions. In Proceedings of the 14th1 and 15th Asian Logic Conferences, pages 213-248. World Sci. Publ., Hackensack, NJ, 2019).

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Miguel A. Cardona. 2024-01-31. Soft-linkedness. https://arxiv.org/abs/2402.00144

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