1 Notation and Terminology Throughout this note κ is always a regular uncountable cardinal, and λ≥κ acardinal. When we say an ideal I on P_κλ, it means that I is a κ-completenon-principal fine ideal on P_κλ. ...1 Notation and Terminology Throughout this note κ is always a regular uncountable cardinal, and λ≥κ acardinal. When we say an ideal I on P_κλ, it means that I is a κ-completenon-principal fine ideal on P_κλ. If M is a ground model of ZFC, then Ult_U(M)denotes the ultrapower of M associated with U, an ultrapower on P_κλ. Let I be an ideal on P_κλ. We consider the generic extension of M given by thecompletion of Boolean algebra P(P_κλ)/I, i.e. forcing with【R(I),≤_I), where R(I)展开更多
文摘1 Notation and Terminology Throughout this note κ is always a regular uncountable cardinal, and λ≥κ acardinal. When we say an ideal I on P_κλ, it means that I is a κ-completenon-principal fine ideal on P_κλ. If M is a ground model of ZFC, then Ult_U(M)denotes the ultrapower of M associated with U, an ultrapower on P_κλ. Let I be an ideal on P_κλ. We consider the generic extension of M given by thecompletion of Boolean algebra P(P_κλ)/I, i.e. forcing with【R(I),≤_I), where R(I)
