Scott formulated his version of Boolean-valued models in 1967, He proved that the V<sup>(B)</sup> is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then...Scott formulated his version of Boolean-valued models in 1967, He proved that the V<sup>(B)</sup> is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, V<sup>(B)</sup> GCH (see [1]). In this note we construct the model △<sup>(B)</sup> on the basis of V<sup>(B)</sup>. Our main results are:(1)△<sup>(B)</sup>) is a Booleanvalued model of GB. (2) Assume the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, △<sup>(B)</sup> GCH. (3) The maximum and minimum principle is true in △<sup>(B)</sup>. (4) △<sup>(B)</sup>(B≠{0, 1}) is a Boolean-valued model of QM.展开更多
文摘Scott formulated his version of Boolean-valued models in 1967, He proved that the V<sup>(B)</sup> is a Boolean-valued model of ZFC, i. e. every axiom of ZFC has Boolean value 1, and assumed the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, V<sup>(B)</sup> GCH (see [1]). In this note we construct the model △<sup>(B)</sup> on the basis of V<sup>(B)</sup>. Our main results are:(1)△<sup>(B)</sup>) is a Booleanvalued model of GB. (2) Assume the GCH. Then, if B satisfies ccc and |B|=2<sup>No</sup>, △<sup>(B)</sup> GCH. (3) The maximum and minimum principle is true in △<sup>(B)</sup>. (4) △<sup>(B)</sup>(B≠{0, 1}) is a Boolean-valued model of QM.