We show that many large cardinal notions up to measurability can be characterized through the existence of certain filters for small models of set theory. This correspondence will allow us to obtain a canonical way in which to assign ideals to many large cardinal notions. This assignment coincides with classical large cardinal ideals whenever such ideals had been defined before. Moreover, in many important cases, relations between these ideals reflect the ordering of the corresponding large cardinal properties both under direct implication and consistency strength.

中文翻译：

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小型模型，大型枢机主教和理想理想

我们表明，通过可用于集合论小型模型的某些过滤器的存在，可以表征许多可度量的大基数概念。这种对应关系将使我们获得将理想分配给许多大型基本概念的规范方法。只要以前已经定义了这种理想，就与古典大基数理想相吻合。此外，在许多重要情况下，这些理想之间的关系反映了在直接影响和一致性强度下相应大基数特性的顺序。