Abstract
We show how to construct, via forcing, splitting families that are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cichoń’s diagram, \(\mathfrak{m}\) (2-Knaster), \(\mathfrak{p}\), \(\mathfrak{h}\), the splitting number \(\mathfrak{s}\) and the reaping number \(\mathfrak{r}\).
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This work was supported by the following grants: Austrian Science Fund (FWF): project number I3081, P29575 (first author); P30666 (second author); Grant-in-Aid for Early Career Scientists 18K13448, Japan Society for the Promotion of Science (third author); Israel Science Foundation (ISF) grant no: 1838/19 (fourth author). This is publication number 1199 of the fourth author.
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Goldstern, M., Kellner, J., Mejía, D.A. et al. Preservation of splitting families and cardinal characteristics of the continuum. Isr. J. Math. 246, 73–129 (2021). https://doi.org/10.1007/s11856-021-2237-7
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DOI: https://doi.org/10.1007/s11856-021-2237-7