Controlling cardinal characteristics without adding reals
We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber.
2019 ◽
Vol 60
(1)
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pp. 61-95
2017 ◽
Vol 56
(7-8)
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pp. 1045-1103
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1998 ◽
Vol 63
(8)
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pp. 1187-1201
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