用超幂构造力迫扩充

CONSTITUTING FORCING EXTERSION WITH ULTRAPOWER

设M是ZFC的可数标准传递模型,B是M上的完全布尔代数,I是B的单位元,G是B上的generic超滤,则有:1) 若A=■M_i(■i∈I(M_i≡M)),A上定义关系R,E,L(A)={∈,=}∪{f|f∈A}(f是f的名)是力迫语言,那么<A,R,E>是L(A)的布尔值模型;2) 若A/G上定义关系∈■,则<A/G,∈■>是M的力迫扩充M[G];3) M[G]=ZFC+ CH。

Let M be a coutable standard transitive model, Bacomplete Boolean algebra in M, Iaunity element of B and G a generic ultrafiltcr in B, then 1) IfA=■M_i (■i∈I) (M_i=M), R, E are relations defined in A and L(A)={∈,=}( ){f|f∈A}(where f is a name of f) is a forcing language, then <A, R, E> is a Boolean value model of L (A); 2) If ∈~* =~* are relations defined in A/ G, then <A/G, ∈~*,=~*> is a forcing extension M[G] of M; 3) M[G]=ZFC+ CH.