Singularizing successor cardinals by forcing
Singularizing successor cardinals by forcing
复制标题
通过强迫来单一化继任枢机主教
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
P. Koepke
中科院分区：
文献类型：
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作者：
D. Adolf;Arthur W. Apter;P. Koepke
。我们展示了集合论的模型，使用大的基数和强迫，其中后续的基数可以通过一些像Namba一样的进一步的集合强迫而变得奇异，在大多数情况下不会将低于该继任基数的基数折叠。对于规则基数的后继者，我们从地面模型中的一致性最优假设开始工作。单数基数的继任者需要更强的假设。我们的偏序不同于Woodin的静止塔强迫，它在对正则基数的后继者进行奇化时需要更强的假设，并且在奇化奇基数的后继者时使基数的余性改变的基数在基数之上塌陷(fffi)。
. We exhibit models of set theory, using large cardinals and forcing, in which successor cardinals can be made singular by some “Namba-like” further set forcing, in most cases without collapsing cardinals below that successor cardinal. For successors of regular cardinals, we work from consistency-wise optimal assumptions in the ground model. Successors of singular cardinals require stronger hypotheses. Our partial orderings are different from Woodin’s stationary tower forcing, which requires much stronger hypotheses when sin-gularizing successors of regular cardinals, and collapses cardinals above the cardinal whose cofinality is changed when singularizing successors of singular cardinals.