超紧性对超紧基数的Mitchell等级
Mitchell rank for supercompactness
AI总结：
本文研究了如何通过forcing技术降低超紧基数的超紧性Mitchell等级，并探讨了相关强紧基数的性质。
摘要：
本文定义了超紧基数的Mitchell等级。如果κ是θ-超紧基数，那么o_{θ-sc}(κ) = sup { o_{θ-sc}(μ) + 1 | μ∈m(κ) }，其中m(κ)是P_κθ上的正常细测度集合。我们展示了如何通过forcing将可测基数κ的度降低到任意指定的度，该度小于等于在原始模型中的度。我们还将展示如何软性地将任何超紧基数的超紧性Mitchell等级降低到任意期望的度，该度小于等于其在原始模型中的度，并且还涉及关于强紧基数的一些结果。
英文摘要：
This paper defines a Mitchell rank for supercompact cardinals. If $κ$ is a $θ$-supercompact cardinal then $o_{θ-sc}(κ) = \sup \{ o_{θ-sc}(μ) + 1 \ | \ μ\in m(κ)\}$, where $m(κ)$ is the collection of normal fine measures on $P_κθ$. We show how to force to kill the degree of a measurable cardinal $κ$ to any specified degree which is less than or equal to the degree of $κ$ in the ground model. We will also show how to softly kill the Mitchell rank for supercompactness of any supercompact cardinal so that in the forcing extension it is any desired degree less than or equal to its degree in the ground model, along with some results concerning strongly compact cardinals.
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。
