Controlling cardinal characteristics without adding reals

Martin Goldstern, Jakob Kellner, Diego A. Mejía*, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Article number2150018
JournalJournal of Mathematical Logic
Volume21
Issue number3
DOIs
StatePublished - 1 Dec 2021

Bibliographical note

Publisher Copyright:
© 2021 World Scientific Publishing Company.

Keywords

  • Cardinal characteristics of the continuum
  • Cichoń's diagram
  • forcing extensions without new reals

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