论文标题
PCF理论和Tukey Spectrum
PCF Theory and the Tukey Spectrum
论文作者
论文摘要
在本文中，我们研究了Tukey Order和PCF理论之间的关系，该关系应用于常规红衣主教。我们表明，对于所有集合$ a $的常规红衣主教是一致的，$ a $ a $，表示为$ \ permatatorname {spec}（a）$的Tukey Spectrum spectrum spectrum a $ a $ a $ a $ a $ a $ a $ a $ a $ a，表示为$ \ operatateName {pcf}（pcf}（a）$;这是根据$ \ mathsf {zfc} $事实来阅读的，事实是$ \ operatatorName {pcf}（a）\ subseteq \ operatateRatorName {spec}（a）$都保留了所有$ a $。我们还证明了何时必须在Tukey Spectrum中进行常规限额红衣主教，或者必须超出一些$ a $的tukey频谱，我们证明了这些相关性对于可能将$ \ operatatorName {spec}（a）$从$ \ operatateName {pcf}（a）$分开的强制性。最后，我们表明，Tukey Spectrum的强部分可以代替PCF理论量表，以将Jonsson代数的存在从下方的下数来抬高以保持其继任者。我们结束了一些问题列表。
In this paper, we investigate the relationship between the Tukey order and PCF theory, as applied to sets of regular cardinals. We show that it is consistent that for all sets $A$ of regular cardinals that the Tukey spectrum of $A$, denoted $\operatorname{spec}(A)$, is equal to the set of possible cofinalities of $A$, denoted $\operatorname{pcf}(A)$; this is to be read in light of the $\mathsf{ZFC}$ fact that $\operatorname{pcf}(A)\subseteq\operatorname{spec}(A)$ holds for all $A$. We also prove results about when regular limit cardinals must be in the Tukey spectrum or must be out of the Tukey spectrum of some $A$, and we show the relevance of these for forcings which might separate $\operatorname{spec}(A)$ from $\operatorname{pcf}(A)$. Finally, we show that the strong part of the Tukey spectrum can be used in place of PCF-theoretic scales to lift the existence of Jonsson algebras from below a singular to hold at its successor. We close with a list of questions.
