Extensions with the approximation and cover properties have no new large cardinals
Extensions with the approximation and cover properties have no new large cardinals
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具有近似和覆盖属性的扩展没有新的大基数
DOI：
10.4064/fm180-3-4
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发表时间：
2003
影响因子：
0.6
通讯作者：
J. Hamkins
中科院分区：
文献类型：
--
作者：
J. Hamkins
如果V的扩张Vbar满足delta近似和类的覆盖性质，并且V是Vbar中的类，则Vbar中的每个适当封闭的嵌入j：Vbar到Nbar，其临界点在delta之上，限制为嵌入j| V：V到N服从于基础模型V。因此，在这样的扩展中，没有新的大基数高于δ。这一结果扩展了数学LO/9808011中的工作。
If an extension Vbar of V satisfies the delta approximation and cover properties for classes and V is a class in Vbar, then every suitably closed embedding j:Vbar to Nbar in Vbar with critical point above delta restricts to an embedding j|V:V to N amenable to the ground model V. In such extensions, therefore, there are no new large cardinals above delta. This result extends work in math.LO/9808011.