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Distributive proper forcing axiom and a left-right dichotomy of Cichoń’s diagram. (English) Zbl 1436.03253

Summary: 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.

MSC:

03E17 Cardinal characteristics of the continuum
03E35 Consistency and independence results
03E50 Continuum hypothesis and Martin’s axiom
03E57 Generic absoluteness and forcing axioms
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