Soft-linkedness

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).