论文标题
Galvin的大型红衣主教的财产和分区的申请
Galvin's property at large cardinals and an application to partition calculus
论文作者
论文摘要
在本文的第一部分中，我们探索了一个非常大的红衣主教$κ$携带$κ$ complete ultrafter的可能性，而没有加尔文的财产。在这种情况下，我们证明了每个接地模型$κ$ complete Ultrafter的一致性延伸到非加尔文蛋白。相反，每个地面型号$κ$ complete Ultrafter都将延伸到$ p $ - 点Ultrafter，因此，另一个满足Galvin的财产，这也是一致的。最后，我们将此属性应用于分区$λ\ rightarrow（λ，ω+1）^2 $中的经典问题的一致新实例。
In the first part of this paper, we explore the possibility for a very large cardinal $κ$ to carry a $κ$-complete ultrafilter without Galvin's property. In this context, we prove the consistency of every ground model $κ$-complete ultrafilter extends to a non-Galvin one. Oppositely, it is also consistent that every ground model $κ$-complete ultrafilter extends to a $P$-point ultrafilter, hence to another one satisfying Galvin's property. Finally, we apply this property to obtain consistently new instances of the classical problem in partition calculus $λ\rightarrow(λ,ω+1)^2$.
