Proper forcing extensions and Solovay models
Proper forcing extensions and Solovay models
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适当的强制扩展和 Solovay 模型
DOI：
10.1007/s00153-003-0210-2
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发表时间：
2004
影响因子：
0.3
通讯作者：
R. Bosch
中科院分区：
文献类型：
--
作者：
J. Bagaria;R. Bosch
我们研究了在适当的射影强迫扩张下，Solovay模型的性质的保持。我们证明了每一个强真强迫概念都保留了这一性质。这就产生了强真强迫概念下绝对性的一致性强度是存在一个不可接近的基数的一致性强度。此外，相对于a-Mahlo基数的存在，欠射影强真强迫概念的绝对性是一致的。我们还证明了下强迫扩张的绝对性与σ关联的强迫概念的一致性强度恰好等于存在一个Mahlo基数，而一般的CCC情形需要一个弱紧的基数。
We study the preservation of the property of being a Solovay model under proper projective forcing extensions. We show that every strongly-proper forcing notion preserves this property. This yields that the consistency strength of the absoluteness of under strongly-proper forcing notions is that of the existence of an inaccessible cardinal. Further, the absoluteness of under projective strongly-proper forcing notions is consistent relative to the existence of a -Mahlo cardinal. We also show that the consistency strength of the absoluteness of under forcing extensions with σ-linked forcing notions is exactly that of the existence of a Mahlo cardinal, in contrast with the general ccc case, which requires a weakly-compact cardinal.