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Omer Ben-Neria (Hebrew University of Jerusalem)

Category
Models and Sets Seminar
Date
Date
Tuesday 31 May 2022, 2:00 PM
Location
MALL

Diamonds, Compactness, and Global Scales

In pursuit of an understanding of the relations between compactness and approximation principles we address the question: To what extent do compactness principles assert the existence of a diamond sequence? It is well known that a cardinal $\kappa$ that satisfies a sufficiently strong compactness assumption must also carry a diamond sequence. However, other results have shown that certain weak large cardinal assumptions are consistent with the failure of the full diamond principle. We will discuss this gap and describe recent results with Jing Zhang which connect this problem to the existence of a certain global notion of cardinal arithmetic scales.