论文标题
有限的共生和向上反思
Bounded Symbiosis and Upwards Reflection
论文作者
论文摘要
Bagaria和Väänänen开发了一个框架，用于研究向下löwenheim-skolems and Resident设置理论反射属性的大型基本强度。主要工具是共生的概念，最初是由第三作者提出的。 共生提供了一种将强大逻辑的理论特性与集合理论中的确定性联系起来的方法。在本文中，我们继续对共生的系统研究，并将其应用于向上的Löwenheim-Skolem定理和反思原则。为了实现这一目标，我们需要将共生的概念调整为一种称为有界共生的新形式。作为一种简单的应用，我们获得了二阶逻辑的较大的löwenheim-skolem-skolem型原理的大型基本强度的上限和下限。
Bagaria and Väänänen developed a framework for studying the large cardinal strength of downwards Löwenheim-Skolem theorems and related set theoretic reflection properties. The main tool was the notion of symbiosis, originally introduced by the third author. Symbiosis provides a way of relating model theoretic properties of strong logics to definability in set theory. In this paper we continue the systematic investigation of symbiosis and apply it to upwards Löwenheim-Skolem theorems and reflection principles. To achieve this, we need to adapt the notion of symbiosis to a new form, called bounded symbiosis. As one easy application, we obtain upper and lower bounds for the large cardinal strength of upwards Löwenheim-Skolem-type principles for second order logic.
