Distributive proper forcing axiom and a left-right dichotomy of Cichon's diagram  

作　　者：Huiling Zhu 

机构地区：[1]School of Data and Computer Science, Sun Yat-sen University

出　　处：《Science China Mathematics》2018年第4期677-684,共8页中国科学：数学（英文版）

摘　　要：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.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.

关 键 词：forcing axiom Cichon＇s diagram preservation 

分 类 号：O156[理学—数学]