Controlling cardinal characteristics without adding reals

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 Cichoń'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.

This is a variant of arXiv:1904.02617 which does not require large cardinals, as it it based on arXiv:1906.06608 instead of arXiv:1708.03691

Cited by in corpus (2)

• Preservation of splitting families and cardinal characteristics of the continuum
• Cichoń's maximum with evasion number