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arXiv · 2006.09826

Controlling cardinal characteristics without adding reals

Martin Goldstern·Jakob Kellner·Diego A. Mejía·Saharon Shelah
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Abstract

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new ${<}\kappa$-sequences (for some regular $\kappa$). As an application, we show that consistently the following cardinal characteristics can be different: The ("independent") characteristics in Cicho\'n's diagram, plus $\aleph_1<\mathfrak m<\mathfrak p<\mathfrak h<\mathrm{add}(\mathcal{N})$. (So we get thirteen different values, including $\aleph_1$ and continuum). We also give constructions to alternatively separate other MA-numbers (instead of $\mathfrak m$), namely: MA for $k$-Knaster from MA for $k+1$-Knaster; and MA for the union of all $k$-Knaster forcings from MA for precaliber.

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Martin Goldstern, Jakob Kellner, Diego A. Mejía, Saharon Shelah. 2020-05-15. Controlling cardinal characteristics without adding reals. https://doi.org/10.1142/s0219061321500185

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