Distributive proper forcing axiom and a left-right dichotomy of Cichoń’s diagram
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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.
Keywordsforcing axiom Cichoń’s diagram preservation
MSC(2010)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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