TY - JOUR
T1 - Controlling cardinal characteristics without adding reals
AU - Goldstern, Martin
AU - Kellner, Jakob
AU - Mejía, Diego A.
AU - Shelah, Saharon
N1 - Publisher Copyright:
© 2021 World Scientific Publishing Company.
PY - 2021/12/1
Y1 - 2021/12/1
N2 - We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences (for some regular κ). As an application, we show that consistently the following cardinal characteristics can be different: The ("independent") characteristics in Cichoń's diagram, plus N1 < < < < add(N). (So we get thirteen different values, including N1 and continuum). We also give constructions to alternatively separate other MA-numbers (instead of ), 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.
AB - We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences (for some regular κ). As an application, we show that consistently the following cardinal characteristics can be different: The ("independent") characteristics in Cichoń's diagram, plus N1 < < < < add(N). (So we get thirteen different values, including N1 and continuum). We also give constructions to alternatively separate other MA-numbers (instead of ), 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.
KW - Cardinal characteristics of the continuum
KW - Cichoń's diagram
KW - forcing extensions without new reals
UR - http://www.scopus.com/inward/record.url?scp=85098544460&partnerID=8YFLogxK
U2 - 10.1142/S0219061321500185
DO - 10.1142/S0219061321500185
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AN - SCOPUS:85098544460
SN - 0219-0613
VL - 21
JO - Journal of Mathematical Logic
JF - Journal of Mathematical Logic
IS - 3
M1 - 2150018
ER -