Science China Mathematics

, Volume 61, Issue 4, pp 677–684 | Cite as

Distributive proper forcing axiom and a left-right dichotomy of Cichoń’s diagram



In this paper, we study distributive proper forcing axiom (DPFA) and prove its consistency with a dichotomy of the Cichoń’s diagram, relative to certain large cardinal assumption. Namely, we evaluate the cardinal invariants in Cichoń’s diagram with the first two uncountable cardinals in the way that the left-hand side has the least possible cardinality while the right-hand side has the largest possible value, and preserve the evaluation along the way of forcing DPFA.


forcing axiom Cichoń’s diagram preservation 


03E17 03E35 03E50 


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The author thanks Institute of Mathematical Science, National University of Singapore for support. The author thanks the reviewers for the suggestions and comments which greatly improved the manuscript. The author is inspired by many people when writing this paper. Among others, the author thanks Professor Qi Feng for his consistent encouragement. Last but foremost, the author thanks his parents for their love and dedicates this work to them.


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© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Data and Computer ScienceSun Yat-sen UniversityGuangzhouChina

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