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ML Seminar

Wintersemester 2020/21

17 December 2020
Yurii Khomskii (Amsterdam & Hamburg)
Bounded Symbiosis and Upwards Reflection

In [1], Bagaria and Väänänen developed a framework for studying the large cardinal strength of Löwenheim-Skolem theorems of strong logics using the notion of Symbiosis (originally introduced by Väänänen in [2]). Symbiosis provides a way of relating model theoretic properties of strong logics to definability in set theory. We continue the systematic investigation of Symbiosis and apply it to upwards Löwenheim-Skolem theorems and upwards reflection principles. To achieve this, the notion of Symbiosis is adapted to what we call "Bounded Symbiosis". As an application, we provide some upper and lower bounds for the large cardinal strength of upwards Löwenheim-Skolem principles of second order logic.

This is joint work with Lorenzo Galeotti and Jouko Väänänen.

[1] Joan Bagaria and Jouko Väänänen, "On the Symbiosis Between Model-Theoretic and Set-Theoretic Properties of Large Cardinals", Journal of Symbolic Logic 81 (2), 584–604.

[2] Jouko Väänänen, "Abstract logic and set theory. I. Definability." In: Logic Colloquium '78 (Mons, 1978), vol. 97 of Studies in Logic and the Foundations of Mathematics (North Holland, 1979), 391–421.

  Seitenanfang  Impress 2020-12-04, B.L.