PP-2020-13: Bounded Symbiosis and Upwards Reflection

PP-2020-13: Galeotti, Lorenzo and Khomskii, Yurii and Väänänen, Jouko (2020) Bounded Symbiosis and Upwards Reflection. [Pre-print] (Submitted)

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Bagaria and V\"a\"an\"anen developed a framework for studying the large cardinal strength of \emph{downwards} L\"owenheim-Skolem theorems and related set theoretic reflection properties. The main tool was the notion of \emph{symbiosis}, originally introduced by the third author.

Symbiosis provides a way of relating model theoretic properties of strong logics to definability in set theory. In this paper we continue the systematic investigation of symbiosis and apply it to upwards L\"owenheim-Skolem theorems and reflection principles. To achieve this, we need to adapt the notion of symbiosis to a new form, called bounded symbiosis. As one easy application, we obtain upper and lower bounds for the large cardinal strength of upwards L\"owenheim-Skolem-type principles for second order logic.

Item Type: Pre-print
Report Nr: PP-2020-13
Series Name: Prepublication (PP) Series
Year: 2020
Subjects: Logic
Depositing User: lgaleot1
Date Deposited: 02 Aug 2020 18:12
Last Modified: 02 Aug 2020 18:12
URI: https://eprints.illc.uva.nl/id/eprint/1745

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