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
This paper, using the model RΔ(B)-a generalized Boolean-valued model of the axiom system GB (see [3]), proves: (1) some properties of forcing F (2) two important theorems-Forcing Theorem and Generic Model Theorem (of...This paper, using the model RΔ(B)-a generalized Boolean-valued model of the axiom system GB (see [3]), proves: (1) some properties of forcing F (2) two important theorems-Forcing Theorem and Generic Model Theorem (of GB); (3) discussing forcing with proper class.展开更多
Ⅰ. INTRODUCTIONLet ◇ denote the diamond principle, □ the box principle, ST_k a Suslin_k-tree. The report presents a new thorough relation between the above combinatorial principles and the Suslin_k-trees.
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.
文摘This paper, using the model RΔ(B)-a generalized Boolean-valued model of the axiom system GB (see [3]), proves: (1) some properties of forcing F (2) two important theorems-Forcing Theorem and Generic Model Theorem (of GB); (3) discussing forcing with proper class.
文摘Ⅰ. INTRODUCTIONLet ◇ denote the diamond principle, □ the box principle, ST_k a Suslin_k-tree. The report presents a new thorough relation between the above combinatorial principles and the Suslin_k-trees.
