与不可达lambda的空理想类似。部件I
A parallel to the null ideal for inaccessible lambda. Part I
摘要：
众所周知，用（正则）基数lambda > aleph_0替换aleph_0并要求理想是lambda^+-完全的，可以推广稀疏理想。但是我们能推广零理想吗？在强迫方面，这意味着找到一个类似于随机实强迫的力迫概念，用lambda代替aleph_0，因此要求它是（<lambda）-完备的。当然，我们也欢迎将随机实强迫的性质推广的其他性质。回到理想（而不是强迫），我们可以看看布尔代数的布尔-博雷尔集模的理想。令人惊讶的是，我们得到了一个积极的=存在的答案λ a“温和”的大基数：弱紧的。我们应用此方法来获得此类lambda的基数不变量的一致性结果。我们将处理其他红衣主教更多的财产有关的力迫概念在一个延续。
英文摘要：
It is well known to generalize the meagre ideal replacing aleph_0 by a (regular) cardinal lambda > aleph_0 and requiring the ideal to be lambda^+-complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing aleph_0 by lambda, so requiring it to be (<lambda)-complete. Of course, we would welcome additional properties generalizing the ones of the random real forcing. Returning to the ideal (instead forcing) we may look at the Boolean Algebra of lambda-Borel sets modulo the ideal. Surprisingly we get an positive = existence answer for lambda a "mild" large cardinals: the weakly compact ones. We apply this to get consistency results on cardinal invariants for such lambda's. We shall deal with other cardinals more properties related forcing notions in a continuation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
