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Strong logics in set theory and search for singular compactness

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If you have a question about this talk, please contact Benedikt Loewe.

part of STUK 1

In the world of infinite cardinals, combinatorial properties of singular cardinals are somewhat special. This is especially visible by the fact that they often exhibit a compactness behaviour, such as in Shelah’s singular compactness theorem or pcf theorem. The cardinal ℵ0 is also very special, often because of the compactness. An important example is the compactness of the first order logic. Therefore it is natural to ask if there is a compact logic associated to singular cardinals, a question that we explore. This talk reports on results in progress obtained jointly with Jouko Väänänen.

This talk is part of the Set Theory Seminar series.

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