arXiv math/07036472007-03math.LO

关于强负分拆关系的一个注记

A note on strong negative partition relations

Todd Eisworth

备注：: 23 pages. Covers my talk at the AMS meeting at Miami University. This is essentially in final form, and is more than twice the length of the previously circulated version because of many new results. Comments are welcome

摘要：

我们分析了一个在奇异基数上可由尺度定义的自然函数，利用这个函数，我们能够在奇异基数的后继者上得到相当强的负方括号划分关系.我们的主要结果的证明利用俱乐部猜测，并作为推论，我们得到了一个相当容易的证明困难的结果Shelah连接弱饱和一定俱乐部猜测理想与强故障的方括号分割关系。然后，我们研究了这种理想的弱饱和的强度，并得到了一些结果的平稳反射。

英文摘要：

We analyze a natural function definable from a scale at a singular cardinal, and using this function we are able to obtain quite strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main result makes use of club-guessing, and as a corollary we obtain a fairly easy proof of a difficult result of Shelah connecting weak saturation of a certain club-guessing ideal with strong failures of square-brackets partition relations. We then investigate the strength of weak saturation of such ideals and obtain some results on stationary reflection.

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。

摘要：

英文摘要：

相关论文