Colloquium: Yair Hayut (HUJI) — Global Reflection Phenomena and incompatible pairs

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Title: Global Reflection Phenomena and incompatible pairs

Abstract: Reflection principles are statements that insure that some types of properties of a large structure must appear at small sub-structures, where "large" and "small" are measured in terms of cardinality.

These principles are modelled after the typical behavior of the universe around large cardinals. The question whether they can hold at small cardinals is a classical topic in combinatorial set theory in the last few decades. In some sense, this means that small cardinals can behave like large cardinals. 
In this talk I will focus on the problem of obtaining global results. Namely, whether it is possible that some property of a large cardinal holds at all cardinals. In this talk I will give an example of a property for which such a global result is impossible due to the incompatibility of a pair of instances, while every local instance is possible. I will point towards some other cases in which this phenomenon might occur.


Thu, 22/04/2021 - 14:30 to 15:30