In this paper, we study distributive proper forcing axiom(DPFA) and prove its consistency with a dichotomy of the Cichon's diagram, relative to certain large cardinal assumption. Namely, we evaluate the cardinal i...In this paper, we study distributive proper forcing axiom(DPFA) and prove its consistency with a dichotomy of the Cichon's diagram, relative to certain large cardinal assumption. Namely, we evaluate the cardinal invariants in Cichon'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.展开更多
文摘In this paper, we study distributive proper forcing axiom(DPFA) and prove its consistency with a dichotomy of the Cichon's diagram, relative to certain large cardinal assumption. Namely, we evaluate the cardinal invariants in Cichon'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.
