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