论文标题
强大的树特性，kurepa树和猜测模型
Strong tree properties, Kurepa trees, and guessing models
论文作者
论文摘要
我们研究了Weiß和Viale引入的广义树特性和猜测模型特性，以及其自然削弱，研究了这些特性之间以及这些特性与其他突出的组合原理之间的关系。我们介绍了Viale和Weiß的猜测模型属性的削弱，我们称之为几乎猜测的属性，并证明它提供了细长树属性的替代表述，其方式与猜测模型属性提供的方式相同，并提供了无法验证的细长树属性的替代表述。我们表明，几乎猜测财产的实例具有足够的强度，例如，正方形的失败或弱库雷帕树的不存在。我们表明，艾尔莫特（Almsot）猜测属性的这些实例从米切尔（Mitchell）模型中起源于强烈紧凑的基数开始，并证明了许多其他一致性结果表明所考虑的原则之间的某些含义通常是不可逆的。在此过程中，我们通过构建一个模型来为Viale问题提供一个新答案，在该模型中，对于所有常规的$θ\ geqω_2$，在\ in \ Mathscr {p} _ {p} _ {ω_2} h（θ）H（θ）$中，有很多$ω_2$ - guessing型$ m \ in \ mathscr {p} _ {p}
We investigate the generalized tree properties and guessing model properties introduced by Weiß and Viale, as well as natural weakenings thereof, studying the relationships among these properties and between these properties and other prominent combinatorial principles. We introduce a weakening of Viale and Weiß's Guessing Model Property, which we call the Almost Guessing Property, and prove that it provides an alternate formulation of the slender tree property in the same way that the Guessing Model Property provides and alternate formulation of the ineffable slender tree property. We show that instances of the Almost Guessing Property have sufficient strength to imply, for example, failures of square or the nonexistence of weak Kurepa trees. We show that these instances of the Almsot Guessing Property hold in the Mitchell model starting from a strongly compact cardinal and prove a number of other consistency results showing that certain implications between the principles under consideration are in general not reversible. In the process, we provide a new answer to a question of Viale by constructing a model in which, for all regular $θ\geq ω_2$, there are stationarily many $ω_2$-guessing models $M \in \mathscr{P}_{ω_2} H(θ)$ that are not $ω_1$-guessing models.
