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Archive for Mathematical Logic

, Volume 56, Issue 7–8, pp 1045–1103 | Cite as

Creature forcing and five cardinal characteristics in Cichoń’s diagram

  • Arthur Fischer
  • Martin Goldstern
  • Jakob KellnerEmail author
  • Saharon Shelah
Open Access
Article

Abstract

We use a (countable support) creature construction to show that consistently
$$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}(\mathcal N)< {{\mathrm{non}}}(\mathcal M)< {{\mathrm{non}}}(\mathcal N)< {{\mathrm{cof}}}(\mathcal N) < 2^{\aleph _0}. \end{aligned}$$
The same method shows the consistency of
$$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}(\mathcal N)< {{\mathrm{non}}}(\mathcal N)< {{\mathrm{non}}}(\mathcal M)< {{\mathrm{cof}}}(\mathcal N) < 2^{\aleph _0}. \end{aligned}$$

Keywords

Set theory of the reals Creature forcing Cichoń’s diagram 

Mathematics Subject Classification

03E17 03E35 03E40 

Notes

Acknowledgements

Open access funding provided by Austrian Science Fund (FWF). We are grateful to Diego Mejía for pointing out several embarrassing oversights. We also thank the anonymous referee for pointing out additional errors, and making numerous helpful suggestions for improving the text.

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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Arthur Fischer
    • 1
  • Martin Goldstern
    • 2
  • Jakob Kellner
    • 2
    Email author
  • Saharon Shelah
    • 3
    • 4
  1. 1.Kurt Gödel Research Center for Mathematical LogicUniversität WienViennaAustria
  2. 2.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienViennaAustria
  3. 3.Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat RamThe Hebrew University of JerusalemJerusalemIsrael
  4. 4.Department of MathematicsRutgers UniversityNew BrunswickUSA

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