Controlling cardinal characteristics without adding reals

Martin Goldstern; Jakob Kellner; Diego A. Mejía; Saharon Shelah

doi:10.1142/S0219061321500185

Controlling cardinal characteristics without adding reals

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

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

6 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 language	English
Article number	2150018
Journal	Journal of Mathematical Logic
Volume	21
Issue number	3
DOIs	https://doi.org/10.1142/S0219061321500185
State	Published - 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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10.1142/S0219061321500185

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AU - Mejía, Diego A.

AU - Shelah, Saharon

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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

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Controlling cardinal characteristics without adding reals

Abstract

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Keywords

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